Prof. Dr. Günter Last
- Raum: 2.001
CS 20.30 - Tel.: +49 721 608-46698
- guenter last ∂does-not-exist.kit edu
- Englerstr. 2
76131 Karlsruhe
Forschung
Forschungsgebiete
- Stochastische Prozesse und ihre Anwendungen
- Stochastische Geometrie
Promotionen
Die Themen der von mir betreuten Promotionen findet man auf dieser Seite.
DFG-Forschungsgruppe FOR1548
Geometry and Physics of Spatial Random Systems (2011 - 2019)
DFG-Schwerpunktprogramm SPP2265
Random Geometric Systems (seit 2020)
Wissenschaftliche Kurzbiografie
Günter Last hat an der Humboldt-Universität zu Berlin (HUB) von 1979-1984 Mathematik studiert und dort 1987 promoviert.
Bis 1992 war er wissenschaftlicher Mitarbeiter an der HUB.
Danach war er bis 2000 an der Technischen Universität Braunschweig wissenschaftlicher Rat bzw. Oberassistent und hat sich dort 1995 habilitiert. In den Jahren 1995/96 und 1996/97 vertrat er Professuren an der TU Kaiserslautern bzw. an der Universität Bonn.
Seit 2000 ist Günter Last Professor für Mathematische Stochastik (C4, seit 2009 W3) am Karlsruher Institut für Technologie.
Bücher
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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
Weitere Infos zu Lectures on the Poisson Process
Weitere Infos zu den Bänden Mathematik für Wirtschaftsingenieure
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
Publikationen
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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 -
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.
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 -
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.; 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 -
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.
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
weitere Aktivitäten
- Mitherausgeber der Zeitschriften Electronic Journal of Probability und Electronic Communications in Probability (2018-2023)
- Mitherausgeber der Applied Probability Journals (2005-2019)
- Sprecher der DFG-Forschergruppe Geometry and Physics of Spatial Random Systems (2011-2018)
- Mitglied des Vorstands der Fachgruppe Stochastik (2004-2008)
- Mitherausgeber der Zeitschrift Queueing Systems: Theory and Applications (2001-2007)