Prof. Dr. Günter Last
- Room: 2.001
CS 20.30 - Phone: +49 721 608-46698
- guenter last ∂does-not-exist.kit edu
- Englerstr. 2
76131 Karlsruhe
Research
Research areas
- Stochastic processes and their applications
- Stochastic geometry
Doctoral theses
The topics of the doctoral theses I supervised can be found on this page.
DFG Research Group FOR1548
Geometry and Physics of Spatial Random Systems (2011 - 2019)
DFG Priority Program SPP2265
Random Geometric Systems (since 2020)
Condensed CV
Günter Last received the diploma degree in mathematics from Humboldt-University in Berlin in 1984 and the PhD. also from the same university in 1987. He worked there as a scientific assistent till 1992. Then he moved to Technical University in Braunschweig, where he received Dr. Sc. degree in 1995. In 1995/96 he spent one semester as a visiting professor at the University of Kaiserslautern and 1996/97 he spent one year as visiting professor at the University of Bonn. Since 2000 he is professor (C4, since 2009 W3) at the University of Karlsruhe.
Books
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Last, G.; Penrose, M. D.
Lectures on the Poisson Process
2018. Cambridge University Press (CUP). doi:10.1017/9781316104477 -
Last, G.; Brandt, A.
Marked Point Processes on the real line : the dynamical approach
1995. Springer Nature
Further information on Lectures on the Poisson Process
Further information on the volumes Mathematics for Industrial Engineers
Preprints
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Klatt, M. A.; Last, G.; Lotz, L.; Yogeshwaran, D.
Invariant transports of stationary random measures: asymptotic variance, hyperuniformity, and examples
2025. arxiv. doi:10.48550/arXiv.2506.05907 -
Hug, D.; Last, G.; Schulte, M.
Boolean models in hyperbolic space
2024. arxiv. doi:10.48550/arXiv.2408.03890 -
Chebunin, M.; Last, G.
On the uniqueness of the infinite cluster and the cluster density in the Poisson driven random connection model
2024. arxiv. doi:10.48550/arXiv.2403.17762 -
Klatt, M. A.; Last, G.; Henze, N.
A genuine test for hyperuniformity
2022. arxiv. doi:10.48550/arXiv.2210.12790
Publications
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Last, G.; Molchanov, I.; Schulte, M.
Normal Approximation of Kabanov–Skorohod Integrals on Poisson Spaces
2024. Journal of Theoretical Probability, 37 (2), 1124–1167. doi:10.1007/s10959-023-01287-0 -
Last, G.
Tail processes and tail measures: An approach via Palm calculus
2023. Extremes, 26 (4), 715–746. doi:10.1007/s10687-023-00472-y -
Last, G.; Peccati, G.; Yogeshwaran, D.
Phase transitions and noise sensitivity on the Poisson space via stopping sets and decision trees
2023. Random Structures & Algorithms, 63 (2), 457–511. doi:10.1002/rsa.21136 -
Betsch, S.; Last, G.
On the uniqueness of Gibbs distributions with a non-negative and subcritical pair potential
2023. Annales de l’institut Henri Poincare (B) Probability and Statistics, 59 (2), 706–725. doi:10.1214/22-AIHP1265 -
Last, G.; Thorisson, H.
Transportation of diffuse random measures on Rd
2023. Latin American Journal of Probability and Mathematical Statistics, 20 (1), 577–592. doi:10.30757/ALEA.v20-21 -
Klatt, M. A.; Last, G.
On strongly rigid hyperfluctuating random measures
2022. Journal of Applied Probability, 59 (4), 1–14. doi:10.1017/jpr.2022.1 -
Ernesti, F.; Schneider, M.; Winter, S.; Hug, D.; Last, G.; Böhlke, T.
Characterizing digital microstructures by the Minkowski‐based quadratic normal tensor
2022. Mathematical Methods in the Applied Sciences, 46 (1), 961–985. doi:10.1002/mma.8560 -
Last, G.; Nestmann, F.; Schulte, M.
The random connection model and functions of edge-marked poisson processes: Second order properties and normal approximation
2021. Annals of Applied Probability, 31 (1), 128–168. doi:10.1214/20-AAP1585 -
Klatt, M. A.; Last, G.; Yogeshwaran, D.
Hyperuniform and rigid stable matchings
2020. Random structures & algorithms, 57 (2), 439–473. doi:10.1002/rsa.20923 -
Beneš, V.; Hofer-Temmel, C.; Last, G.; Večeřa, J.
Decorrelation of a class of Gibbs particle processes and asymptotic properties of U -statistics
2020. Journal of applied probability, 57 (3), 928–955. doi:10.1017/jpr.2020.51 -
Last, G.; Szekli, R.; Yogeshwaran, D.
Some remarks on associated random fields, random measures and point processes
2020. Alea, 17 (1), 355–374. doi:10.30757/ALEA.V17-14 -
Last, G.
An Integral Characterization of the Dirichlet Process
2020. Journal of theoretical probability, 33, 918–930. doi:10.1007/s10959-019-00923-y -
Henze, N.; Last, G.
Absent-Minded Passengers
2019. The American mathematical monthly, 126 (10), 867–875. doi:10.1080/00029890.2019.1656024 -
Last, G.; Szekli, R.
On negative association of some finite point processes on general state spaces
2019. Journal of applied probability, 56 (1), 139–152. doi:10.1017/jpr.2019.10 -
Last, G.; Penrose, M. D.
Lectures on the Poisson Process
2018. Cambridge University Press (CUP). doi:10.1017/9781316104477 -
Hirsch, C.; Last, G.
On Maximal Hard-Core Thinnings of Stationary Particle Processes
2018. Journal of statistical physics, 170 (3), 554–583. doi:10.1007/s10955-017-1943-3 -
Last, G.; Tang, W.; Thorisson, H.
Transporting random measures on the line and embedding excursions into Brownian motion
2018. Annales de l’Institut Henri Poincaré / B, 54 (4), 2286–2303. doi:10.1214/17-AIHP871 -
Gieringer, F.; Last, G.
Concentration inequalities for measures of a Boolean model
2018. Alea, 15 (1), 151–166. doi:10.30757/ALEA.v15-07 -
Last, G.; Ziesche, S.
On the Ornstein–Zernike equation for stationary cluster processes and the random connection model
2017. Advances in applied probability, 49 (4), 1260–1287. doi:10.1017/apr.2017.41 -
Hug, D.; Klatt, M. A.; Last, G.; Schulte, M.
Second Order Analysis of Geometric Functionals of Boolean Models
2017. Tensor Valuations and Their Applications in Stochastic Geometry and Imaging. Ed.: E. Vedel Jensen, 339–383, Springer International Publishing. doi:10.1007/978-3-319-51951-7_12 -
Klatt, M. A.; Last, G.; Mecke, K.; Redenbach, C.; Schaller, F. M.; Schröder-Turk, G. E.
Cell shape analysis of random tessellations based on Minkowski tensors
2017. Tensor Valuations and Their Applications in Stochastic Geometry and Imaging. Ed.: E. B. Vedel Jensen, 385–421, Springer. doi:10.1007/978-3-319-51951-7_13 -
Last, G.; Penrose, M. D.; Zuyev, S.
On the capacity functional of the infinite cluster of a boolean model
2017. The annals of applied probability, 27 (3), 1678–1701. doi:10.1214/16-AAP1241 -
Kabluchko, Z.; Last, G.; Zaporozhets, D.
Inclusion–Exclusion Principles for Convex Hulls and the Euler Relation
2017. Discrete & computational geometry, 58 (2), 417–434. doi:10.1007/s00454-017-9880-0 -
Last, G.
Stochastic Analysis for Poisson Processes
2016. Stochastic Analysis for Poisson Point Processes : Malliavin Calculus, Wiener-Itô Chaos, Expansions and Stochastic Geometry. Ed.: G. Peccati, 1–36, Springer. doi:10.1007/978-3-319-05233-5_1 -
Daley, D. J.; Ebert, S.; Last, G.
Two lilypond systems of finite line-segments
2016. Probability and mathematical statistics, 36 (2), 221–246 -
Hug, D.; Last, G.; Schulte, M.
Second-order properties and central limit theorems for geometric functionals of Boolean models
2016. The annals of applied probability, 26 (1), 73–135. doi:10.1214/14-AAP1086 -
Last, G.; Peccati, G.; Schulte, M.
Normal approximation on Poisson spaces: Mehler’s formula, second order Poincaré inequalities and stabilization
2016. Probability theory and related fields, 165 (3), 667–723. doi:10.1007/s00440-015-0643-7 -
Ebert, S.; Last, G.
On a class of growth-maximal hardcore processes
2015. Stochastic models, 31 (1), 153–185. doi:10.1080/15326349.2015.973722 -
Last, G.; Thorisson, H.
Construction and characterization of stationary and mass-stationary random measures on Rd
2015. Stochastic processes and their applications, 125 (12), 4473–4488. doi:10.1016/j.spa.2015.07.006 -
Last, G.; Ochsenreither, E.
Percolation on stationary tessellations: models, mean values, and second-order structure
2014. Journal of Applied Probability, 51 (A), 311–332. doi:10.1239/jap/1417528483 -
Hug, D.; Last, G.; Pawlas, Z.; Weil, W.
Statistics for Poisson Models of Overlapping Spheres
2014. Advances in Applied Probability, 46 (4), 937–962. doi:10.1239/aap/1418396238 -
Last, G.; Penrose, M. D.; Schulte, M.; Thaele, C.
Moments and central limit theorems for some multivariate Poisson functionals
2014. Advances in applied probability, 46 (2), 348–364. doi:10.1239/aap/1401369698 -
Last, G.; Mörters, P.; Thorisson, H.
Unbiased shifts of Brownian motion
2014. Annals of Probability, 42 (2), 431–864. doi:10.1214/13-AOP832 -
Last, G.; Penrose, M.
Percolation and limit theory for the Poisson lilypond model
2013. Random Structures & Algorithms, 42 (2), 226–249. doi:10.1002/rsa.20410 -
Borovkov, K. A.; Last, G.
On Rice’s formula for stationary multivariate piecewise smooth processes
2012. Journal of Applied Probability, 49 (2), 351–363. doi:10.1239/jap/1339878791 -
Kampf, J.; Last, G.; Molchanov, I.
On the convex hull of symmetric stable processes
2012. Proceedings of the American Mathematical Society, 140, 2527–2535. doi:10.1090/S0002-9939-2012-11128-1 -
Last, G.; Szekli, R.
Comparisons and asymptotics for empty space hazard functions of germ-grain models
2011. Advances in Applied Probability, 43 (4), 943–962. doi:10.1239/aap/1324045693 -
Last, G.; Penrose, M. D.
Poisson process Fock space representation, chaos expansion and covariance inequalities
2011. Probability Theory and Related Fields, 150 (3-4), 663–690. doi:10.1007/s00440-010-0288-5 -
Last, G.; Thorisson, H.
What is typical?
2011. Journal of Applied Probability, 48 (A), 379–389. doi:10.1239/jap/1318940478 -
Last, G.; Penrose, M. D.
Martingale representation for Poisson processes with applications to minimal variance hedging
2011. Stochastic Processes and their Applications, 121 (7), 1588–1606. doi:10.1016/j.spa.2011.03.014 -
Last, G.; Thorisson, H.
Characterization of mass-stationarity by Bernoulli and Cox transports
2011. Communications on Stochastic Analysis, 5 (2), 251–269. doi:10.31390/cosa.5.2.01 -
Last, G.; Thorisson, H.
What is typical?
2011. Journal of Applied Probability : Special volume, 48A, 379–390 -
Gentner, D.; Last, G.
Palm pairs and the general mass transport principle
2011. Mathematische Zeitschrift, 276 (3-4), 695–716. doi:10.1007/s00209-009-0642-4 -
Bordenave, C.; Foss, S.; Last, G.
On the greedy walk problem
2011. Queueing Systems: Theory and Applications, 68 (3-4), 333–338. doi:10.1007/s11134-011-9246-x -
Last, G.
Stationary random measures on homogeneous spaces
2010. Journal of Theoretical Probability, 23 (2), 478–497. doi:10.1007/s10959-009-0231-9 -
Baumstark, V.; Last, G.
Gamma distributions for stationary Poisson flat processes
2009. Advances in Applied Probability, 41 (4), 911–939. doi:10.1239/aap/1261669578 -
Last, G.
Modern Random Measures: Palm Theory and Related Models
2009. New Perspectives in Stochastic Geometry. Ed.: W. Kendall, 77–110, Oxford University Press (OUP). doi:10.1093/acprof:oso/9780199232574.003.0003 -
Last, G.; Thorisson, H.
Invariant transports of stationary random measures and mass-stationarity
2009. The Annals of Probability, 37 (2), 790–813. doi:10.1214/08-aop420 -
Hoferer, J.; Hoffmann, L. M.; Goebbels, J.; Last, G.; Weil, W.; Kasper, G.
Reconstruction algorithms for the internal packing density distribution of fibrous filter media based on tomographic data
2009. Filtration : the international journal for filtration and separation / The Filtration Society, 9 (2), 147–154 -
Borovkov, K.; Last, G.
On level crossings for a general class of piecewise-deterministic Markov processes
2008. Advances in Applied Probability, 40 (3), 815–834. doi:10.1239/aap/1222868187 -
Baumstark, V.; Last, G.
Some distributional results for Poisson-Voronoi tessellations
2007. Advances in Applied Probability, 39 (1), 16–40. doi:10.1239/aap/1175266467 -
Heveling, M.; Last, G.
Point shift characterization of Palm measures on Abelian groups
2007. Electronic Journal of Probability, 12, 122–137. doi:10.1214/ejp.v12-394 -
Heveling, M.; Last, G.
Existence, uniqueness, and algorithmic computation of general lilypond systems
2006. Random Structures & Algorithms, 29 (3), 338–350. doi:10.1002/rsa.20099 -
Hug, D.; Last, G.; Weil, W.
Polynomial parallel volume, convexity and contact distributions of random sets
2006. Probability Theory and Related Fields, 135 (2), 169–200. doi:10.1007/s00440-005-0459-y -
Last, G.
Stationary partitions and Palm probabilities
2006. Advances in Applied Probability, 38 (3), 602–620 -
Last, G.
On mean curvature functions of Brownian paths
2006. Stochastic Processes and their Applications : Monthly, 116 (12), 1876–1891 -
Heveling, M.; Last, G.
Existence, uniqueness and algorithmic computation of general lilypond systems
2006. Random Structures and Algorithms, 29 (3), 338–350 -
Daley, D. J.; Last, G.
Descending chains, the lilypond model, and mutual-nearest-neighbour matching
2005. Advances in Applied Probability, 37 (3), 604–628. doi:10.1239/aap/1127483738 -
Heveling, M.; Last, G.
Characterization of Palm measures via bijective point-shifts
2005. The Annals of Probability, 33 (5), 1698–1715. doi:10.1214/009117905000000224 -
Last, G.
Ergodicity properties of stress release, repairable system and workload models
2004. Advances in Applied Probability, 36 (2), 471–498. doi:10.1239/aap/1086957582 -
Konstantopoulos, T.; Last, G.; Lin, S.-J.
On a Class of Lévy Stochastic Networks
2004. Queueing Systems, 46 (3-4), 409–437. doi:10.1023/b:ques.0000027993.51077.f2 -
Heveling, M.; Hug, D.; Last, G.
Does polynomial parallel volume imply convexity?
2004. Mathematische Annalen, 328 (3), 469–479. doi:10.1007/s00208-003-0497-7 -
Hug, D.; Last, G.; Weil, W.
A local Steiner–type formula for general closed sets and applications
2004. Mathematische Zeitschrift, 246 (1-2), 237–272. doi:10.1007/s00209-003-0597-9 -
Hug, D.; Last, G.; Weil, W.
Distance measurements on processes of flats
2003. Advances in Applied Probability, 35 (1), 70–95. doi:10.1239/aap/1046366100 -
Hug, D.; Last, G.; Weil, W.
A local Steiner-type formula for general closed sets and applications
2003. Karlsruhe 2003. (Preprint. Fakultät für Mathematik, Universität Karlsruhe. 2003,3.) -
Hug, D.; Last, G.; Weil, W.
Distance measurements on processes of flats
2003. Karlsruhe 2003. (Preprint. Fakultät für Mathematik, Universität Karlsruhe. 2003,2.) -
Hug, D.; Last, G.; Weil, W.
Generalized contact distributions of inhomogeneous Boolean models
2002. Advances in Applied Probability, 34 (1), 21–47. doi:10.1239/aap/1019160948 -
Kabanov, Y. M.; Last, G.
Hedging in a model with transaction costs
2002. Труды Математического института имени ВА Стеклова, 237 (1), 217–223 -
Hug, D.; Last, G.; Weil, W.
A Survey on Contact Distributions
2002. Morphology of Condensed Matter : Physics and Geometry of Spatially Complex Systems. Ed.: K. Mecke, 317–357, Springer-Verlag. doi:10.1007/3-540-45782-8_14 -
Hug, D.; Last, G.; Weil, W.
A survey on contact distributions
2002. Karlsruhe 2002. (Preprint. Fakultät für Mathematik, Universität Karlsruhe. 2002,6.) -
Kabanov, Y. M.; Last, G.
Hedging under transaction costs in currency markets: a continuous-time model
2002. Mathematical finance, 12 (1), 63–70. doi:10.1111/1467-9965.00004 -
Last, G.
Ergodicity properties of a class of Markov modulated renewal processes
2002. Karlsruhe 2002. (Preprint. Fakultät für Mathematik, Universität Karlsruhe. 2002,42.) -
Last, G.; Schassberger, R.
On the second derivative of the spherical contact distribution function of smooth grain models
2001. Probability Theory and Related Fields, 121 (1), 49–72. doi:10.1007/pl00008797 -
Hug, D.; Last, G.; Weil, W.
Generalized contact distributions of inhomogeneous Boolean models
2001. Karlsruhe 2001. (Preprint. Fakultät für Mathematik, Universität Karlsruhe. 2001,9.) -
Last, G.; Szekli, R.
Moments and Blackwell’s convergence for repairable systems with heavy tailed lifetimes
2001. Markov processes and related fields, 7, 469–490 -
Last, G.; Schassberger, R.
On the second derivative of the spherical contact distribution function of smooth grain models
2001. Probability theory and related fields, 121 (1), 49–72 -
Last, G.; Schassberger, R.
On stationary stochastic flows and Palm probabilities of surface processes
2000. The Annals of Applied Probability, 10 (2). doi:10.1214/aoap/1019487351 -
Hug, D.; Last, G.
On support measures in Minkowski spaces and contact distributions in stochastic geometry
2000. The Annals of Probability, 28 (2), 796–850. doi:10.1214/aop/1019160261 -
Konstantopoulos, T.; Last, G.
On the dynamics and performance of stochastic fluid systems
2000. Journal of applied probability, J. of appl. probabil. 37 (2000) S. 652-667., 37 (3), 652–667. doi:10.1239/jap/1014842826 -
Last, G.; Stamer, H.
Recurrence and transience properties of some neural networks: an approach via fluid limit models
1999. Queueing Systems, 32 (1-3), 99–130. doi:10.1023/a:1019135020138 -
Last, G.; Holtmann, M.
On the empty space function of some germ-grain models
1999. Pattern Recognition, 32 (9), 1587–1600. doi:10.1016/s0031-3203(99)00022-9 -
Konstantopoulos, T.; Last, G.
On the use of Lyapunov function methods in renewal theory
1999. Stochastic Processes and their Applications, 79 (1), 165–178. doi:10.1016/s0304-4149(98)00068-4 -
Last, G.; Szekli, R.
Time and Palm stationarity of repairable systems
1999. Stochastic Processes and their Applications, 79 (1), 17–43. doi:10.1016/s0304-4149(98)00067-2 -
Last, G.; Szekli, R.
Asymptotic and monotonicity properties of some repairable systems
1998. Advances in Applied Probability, 30 (4), 1089–1110. doi:10.1239/aap/1035228209 -
Last, G.; Szekli, R.
Stochastic comparison of repairable systems by coupling
1998. Journal of Applied Probability, 35 (2), 348–370. doi:10.1239/jap/1032192852 -
Last, G.; Schassberger, R.
On the distribution of the spherical contact vector of stationary germ-grain models
1998. Advances in Applied Probability, 30 (1), 36–52. doi:10.1239/aap/1035227990 -
Foss, S.; Last, G.
On the Stability of Greedy Polling Systems with General Service Policies
1998. Probability in the Engineering and Informational Sciences, 12 (1), 49–68. doi:10.1017/s0269964800005052 -
Last, G.
Coupling with compensators
1996. Stochastic Processes and their Applications, 65 (2), 147–170. doi:10.1016/s0304-4149(96)00110-x -
Last, G.; Schassberger, R.
A flow conservation law for surface processes
1996. Advances in Applied Probability, 28 (1), 13–28. doi:10.2307/1427911 -
Foss, S.; Last, G.
Stability of polling systems with exhaustive service policies and state-dependent routing
1996. The Annals of Applied Probability, 6 (1), 116–137. doi:10.1214/aoap/1034968068 -
Last, G.; Brandt, A.
Marked Point Processes on the real line : the dynamical approach
1995. Springer Nature -
Last, G.
Predictable projections for point process filtrations
1994. Probability Theory and Related Fields, 99 (3), 361–388. doi:10.1007/bf01199897 -
Last, G.
Filtering of derived point processes
1994. Stochastic Processes and their Applications, 49 (2), 297–329. doi:10.1016/0304-4149(94)90139-2 -
Brandt, A.; Last, G.
On the Pathwise Comparison of Jump Processes Driven by Stochastic Intensities
1994. Mathematische Nachrichten, 167 (1), 21–42. doi:10.1002/mana.19941670103 -
Last, G.
On dependent marking and thinning of point processes
1993. Stochastic Processes and their Applications, 45 (1), 73–94. doi:10.1016/0304-4149(93)90061-8 -
Last, G.
On Bayes’ Formula for Doubly Stochastic Point Process on the Real Half-Line
1991. Statistics, 22 (3), 431–448. doi:10.1080/02331889108802324 -
Last, G.
Some remarks on conditional distributions for point processes
1990. Stochastic Processes and their Applications, 34 (1), 121–135. doi:10.1016/0304-4149(90)90059-2
Further activities
- Co-Editor of the Electronic Journal of Probability and Electronic Communications in Probability (2018-2023)
- Co-editor of the Applied Probability Journals (2005-2019)
- Spokesperson of the DFG research group Geometry and Physics of Spatial Random Systems (2011-2018)
- Member of the board of the Stochastics Division (2004-2008)
- Co-editor of the journal Queueing Systems: Theory and Applications (2001-2007)