### Preprints

M. Heydenreich, R. van der Hofstad, G. Last, K. Matzke (2019):

Lace expansion and mean-field behavior for the random connection model.

arXiv:1908.11356

G. Last, S. Zuyev (2019): Applications of the perturbation formula for Poisson processes to elementary and geometric probability.

arXiv:1907.09552

V. Benes, C. Hofer-Temmel, G. Last, J. Vecera (2019): Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics.

arXiv:1903.06553

G. Last, R. Szekli, D. Yogeshwaran (2019): Some remarks on associated random fields, random measures and point processes.

arXiv:1903.06004

M. Klatt, G. Last, D. Yogeshwaran (2018): Hyperuniform and rigid stable matchings.

arXiv:1810.00265

G. Last, F. Nestmann, M. Schulte (2018): The random connection model and functions of edge-marked Poisson processes: second order properties and normal approximation.

arXiv:1808.01203

### Publications

**77.** G. Last (2019): An integral characterization of the Dirichlet process.

To appear in Journal of Theoretical Probability.

An earlier version is available via arXiv:1803.11465

**76.** G. Last, R. Szekli (2018): On negative association of some finite point processes on general state spaces.

To appear in Advances in Applied Probability. An earlier version is available via arXiv:1803.09663

**75.** N. Henze, G. Last (2018): Absent-minded passengers.

To appear in The American Mathematical Monthly. An earlier version is available via arXiv:1809.10192

**74.** F. Gieringer, G. Last (2018): Concentration inequalities for measures of a Boolean model.

ALEA, Lat. Am. J. Probab. Math. Stat. 15, 151–166. arXiv:1703.04971

**73.** C. Hirsch, G. Last (2018): On maximal hard-core thinnings of stationary particle processes.

Journal of Statistical Physics 170, 554-583. arXiv:1707.00494

**72.** G. Last, W. Tang and H. Thorisson (2018): Transporting random measures on the line and embedding excursions into Brownian motion.

Annales de l’Institut Henri Poincare 54, 2286-2303. arXiv:1608.02016

**71.** G. Last and S. Ziesche (2017): On the Ornstein-Zernike equation for stationary cluster processes and the random connection model.

Advances in Applied Probability, 49, 1260-1287. arXiv:1607.02962

**70.** M. Klatt, G. Last, K. Mecke, C. Redenbach, F.M. Schaller, G.E. Schröder-Turk (2017): Cell shape analysis of random tessellations based on Minkowski tensors.

Tensor Valuations and their Applications in Stochastic Geometry and Imaging (M. Kiderlen, Eva B. Vedel Jensen, eds.), Springer, 2017. arXiv:1606.07653

**69.** D. Hug, M. Klatt, G. Last and M. Schulte (2017): Second order analysis of geometric functionals of Boolean models.

Tensor Valuations and their Applications in Stochastic Geometry and Imaging (M. Kiderlen, Eva B. Vedel Jensen, eds.), Springer, 2017.arXiv:1601.06718

**68.** Z . Kabluchko, G. Last and D. Zaporozhets (2017): Inclusion-exclusion principles for convex hulls and the Euler relation.

Discrete and Computational Geometry, 58, 417-434. arXiv:1603.01357

**67.** G. Last, M.D. Penrose and S. Zuyev (2017): On the capacity functional of the infinite cluster of a Boolean model.

Annals of Applied Probability, 27, 1678-1701. arXiv:1601.04945

**66.** G. Last (2016): Stochastic analysis for Poisson processes.

In: Stochastic Analysis for Poisson Point Processes(G. Peccati and M. Reitzner, eds.), Springer, 2016. arXiv:1405.4416

**65.** G. Last, G. Peccati and M. Schulte (2016): "Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization".

Probability Theory and Related Fields 165, 667-723. arXiv:1401.7568

**64.** D. Hug, G. Last and M. Schulte (2016): "Second order properties and central limit theorems for geometric functionals of Boolean models".

Annals of Applied Probability 26, 73-135, 2016. arXiv:1308.6519

arXiv:1308.6519v2 is an extended version of the paper containing two additional appendices.

**63.** G. Last and H. Thorisson (2015): "Construction and characterisation of stationary and mass-stationary random measures on R^d".

Stochastic Processes and their Applications, 125, 4473-4488, 2015. arXiv:1405.7566

**62.** D.J. Daley, S. Ebert, G. Last (2016): "Two lilypond systems of finite line-segments".

Probability and Mathematical Statistics 36, 221-246. arXiv:1406.0096

**61.** S. Ebert and G. Last (2015): On a class of growth-maximal hard-core processes.

Stochastic Models 31, 153-184. arXiv:1303.2092

**60.** G. Last, M.D. Penrose, M. Schulte and C. Thaele (2014): "Moments and central limit theorems for some multivariate Poisson functionals".

Adv. in Appl. Probab. 46, 348-364. arXiv: 1205.3033v1

**59.** D. Hug, G. Last, Z. Pawlas and W. Weil (2014): "Statistics for Poisson models of overlapping spheres".

Advances in Applied Probability, 46, 937-962. arXiv:1301.1499

**58.** G. Last, E. Ochsenreither (2014): "Percolation on stationary tessellations: models, mean values and second order structure".

Journal of Applied Probability, 51A, 311-332. arXiv:1312.6366

**57.** G. Last (2014): "Perturbation analysis of Poisson processes".

Bernoulli 20, 486-513. arXiv:1203.3181

**56.** G. Last, P. Mörters, H. Thorisson (2014): "Unbiased shifts of Brownian motion".

Annals of Probability 2014, Vol. 42, No. 2, 431-463. arXiv:1112.5373

**55.** G. Last and M. Penrose (2013): "Percolation and limit theory for the Poisson lilypond model".

Random Structures Algorithms 42 (2013) 226–249. arXiv:1008.0769v1

**54.** J. Kampf, G. Last and I. Molchanov (2012): "On the convex hull of symmetric stable processes".

Proc. Amer. Math. Soc. 140, 2527-2535. pdf

**53.** K.A. Borovkov and G. Last (2012): "On Rice's formula for stationary multivariate piecewise smooth processes".

Journal of Applied Probability, 49, 351-363. arXiv:1009.3885v1

**52.** G. Last and R. Szekli (2011): "Comparisons and asymptotics for empty space hazard functions of germ-grain models".

Adv. in Appl. Probab. 43, 943-962. arXiv:1012.3056v1

**51.** G. Last and M. Penrose (2011): "Martingale representation for Poisson processes with applications to minimal variance hedging".

Stochastic Processes and their Applications, 121, 1588-1606. arXiv:1001.3972v1

**50.** C. Bordenave, S. Foss and G. Last (2011): "On the greedy walk problem".

Queueing Systems: Theory and Applications 68, 333-338. pdf

**49.** G. Last and H. Thorisson (2011): "What is typical?"

Journal of Applied Probability 48A (Special Volume), 379-390. arXiv:1103.0092v1

**48.** G. Last and H. Thorisson (2011): "Characterization of mass-stationarity by Bernoulli and Cox transports".

Communications on Stochastic Analysis 5, 251-269. pdf

**47.** G. Last and M. Penrose (2011): "Poisson process Fock space representation, chaos expansion and covariance inequalities".

Probability Theory and Related Fields. 150, 663-690.

DOI: 10.1007/s00440-010-0288-5. An earlier version is available via arXiv:0909.3205v1.

**46.** D. Gentner and G. Last (2011): "Palm pairs and the general mass transport principle".

Mathematische Zeitschrift 267, 695-716. An earlier version is available via arXiv:0902.0068v2.

**45.** G. Last (2010): "Stationary random measures on homogeneous spaces".

Journal of Theoretical Probability 23, 478-497. DOI: 10.1007/s10959-009-0231-9. pdf

**44.** G. Last (2010): "Modern random measures: Palm theory and related models". New Perspectives in Stochastic Geometry (W. Kendall und I. Molchanov, eds.),

Oxford University Press, 2010. pdf

**43.** J. Hoferer, L.M. Hoffmann, J. Goebbels, G. Last, W. Weil and G. Kasper (2009): "Reconstruction algorithms for the internal packing density distribution of fibrous filter media based on tomographic data".

Filtration 9, 147-154.

**42.** V. Baumstark and G. Last (2009): "Gamma distributions for stationary Poisson flat processes".

Advances in Applied Probability 41, 911-939. pdf

**41.** G. Last and H. Thorisson (2009): "Invariant transports of stationary random measures and mass-stationarity",

Annals of Probability 37, 790-813. (electronic reprint in ArXiv)

**40. ** K. Borovkov and G. Last (2008): "On level crossings for a general class of piecewise-deterministic Markov processes",

Advances in Applied Probability 40, 815-834.

**39.** M. Heveling and G. Last (2007): "Point shift characterization of Palm measures on Abelian groups",

Electronic Journal of Probability, 12, 122-137. pdf

**38.** V. Baumstark and G. Last (2007): "Some distributional results for Poisson Voronoi tessellations",

Advances in Applied Probability 39, 16-40.

**37.** G. Last (2006): "On mean curvature functions of Brownian paths",

Stochastic Processes and their Applications, 116, 1876-1891.

**36.** G. Last (2006): "Stationary partitions and Palm probabilities",

Advances in Applied Probability, 38, 602-620.

**35.** M. Heveling and G. Last (2006): "Existence, uniqueness and algorithmic computation of general lilypond systems",

Random Structures & Algorithms, 29, 338-350.

**34.** D. Hug, G. Last and W. Weil (2006): "Polynomial parallel volume, convexity and contact distributions of random sets",

Probability Theory and Related Fields, 135, 169-200. pdf

**33.** M. Heveling and G. Last (2005): "Characterization of Palm measures via bijective point-shifts",

Annals of Probability 33, 1698-1715. pdf

**32.** D. Daley and G. Last (2004): "Descending chains, the lilypond model, and mutual nearest neighbour matching",

Advances in Applied Probability, 37, 604-628.

**31.** T. Konstantopoulos, G. Last and S. Lin (2004): "On a class of Lévy stochastic networks",

Queueing Systems, 46, 409-437. pdf

**30.** G. Last (2004): "Ergodicity properties of stress release, repairable system and workload models",

Advances in Applied Probability, 36, 471-498.

**29.** D. Hug, G. Last and W. Weil (2004): "A local Steiner-type formula for general closed sets and applications",

Mathematische Zeitschrift, 246, 237-272. pdf

**28.** M. Heveling, D. Hug and G. Last (2004): "Does parallel volume imply convexity?",

Mathematische Annalen, 328, 469-479. pdf

**27. ** Y.M. Kabanov and G. Last: "Hedging in a model with transaction costs",

Proceedings of Steklov Institute of Mathematics, 237, 208-214, 2003.

**26.** D. Hug, G. Last and W. Weil: "Distance measurements on processes of flats",

Advances in Applied Probability, 35, 70-95, 2003. pdf

**25.** D. Hug, G. Last and W. Weil: "A survey on contact distributions", Morphology of Condensed Matter. Physics and Geometry of Spatially Complex Systems. (K. Mecke, D. Stoyan, eds.), Lecture Notes in Physics, 317-357, Springer, Berlin, 2002. pdf

**24. ** D. Hug, G. Last and W. Weil: "Generalized contact distributions of inhomogeneous Boolean models",

Advances in Applied Probability, 34, 21-47, 2002. pdf

**23. ** Y.M. Kabanov and G. Last: "Hedging under transaction costs in currency markets: a continuous-time model",

Mathematical Finance, 12, 63-70, 2002.

**22.** G. Last and R. Szekli: "Moments and Blackwell's convergence for repairable systems with heavy tailed lifetimes",

Markov Processes and Related Fields, 7, 469-490, 2001.

**21.** G. Last and R. Schassberger: "On the second derivative of the spherical contact distribution function of smooth grain models",

Probability Theory and Related Fields, 121, 49-72, 2001.

**20.** T. Konstantopoulos and G. Last: "On the dynamics and performance of stochastic fluid systems",

Journal of Applied Probability, 37, 652-667, 2000.

**19.** D. Hug and G. Last: "On support measures in Minkowski spaces and contact distributions in stochastic geometry",

Annals of Probability, 28, 796-850, 2000. pdf

**18.** G. Last and R. Schassberger: "On stationary stochastic flows and Palm probabilities of surface processes",

Annals of Applied Probability, 10, 463-492, 2000.

**17.** G. Last and H. Stamer: "Recurrence and transience properties of some neural networks: an approach via fluid limit models",

Queueing Systems, 32, 99-130, 1999.

**16. ** T. Konstantopoulos and G. Last: "On the use of Lyapunov function methods in renewal theory",

Stochastic Processes and their Applications 79, 165-178, 1999.

**15.** G. Last and M. Holtmann : "On the empty space function of some germ-grain models",

Pattern Recognition 32, 1587-1600, 1999.

**14.** G. Last and R. Szekli: "Time and Palm stationarity of repairable systems",

Stochastic Processes and their Applications 79, 17-43, 1999.

**13. ** G. Last and R. Szekli: "Asymptotic and monotonicity properties of some repairable systems",

Advances in Applied Probability 30, 1089-1110, 1998.

**12.** S. Foss and G. Last: "On the stability of greedy polling systems with general service policies",

Probability in the Engineering and Informational Sciences 12, 49 - 68, 1998.

**11.** G. Last and R. Szekli: "Stochastic comparison of repairable systems by coupling",

Journal of Applied Probability 35, 348 - 370, 1998.

**10.** G. Last and R. Schassberger: "On the distribution of the spherical contact vector of stationary grain models", Advances in Applied Probability 30, 36 - 52, 1998.

**9.** S. Foss and G. Last: "Stability of polling systems with exhaustive service policies and state dependent routing",

Annals of Applied Probability 6, 116 - 137, 1996.

**8. ** G. Last: "Coupling with compensators",

Stochastic Process. Appl. 65, 147 - 170, 1996.

**7.** G. Last and R. Schassberger: "A flow conservation law for surface processes",

Advances in Applied Probability 28, 13 - 28, 1996.

**6.** G. Last: "Predictable projections for point process filtrations",

Probability Theory and Related Fields 99, 361-388, 1994.

**5** G. Last: "Filtering of derived point processes",

Stochastic Process. Appl. 49, 297-330, 1994.

**4.** A. Brandt and G. Last : "On the pathwise comparison of jump processes driven by stochastic intensities",

Mathematische Nachrichten 167, 21-42, 1994.

**3.** G. Last: "On dependent marking and thinning of point processes",

Stochastic Process. Appl. 45, 73-94, 1993.

**2.** G. Last: "On Bayes' formula for doubly stochastic point processes on the real half-line",

Statistics 22, 431-448, 1991.

**1.** G. Last: "Some remarks on conditional distributions for point processes",

Stochastic Process. Appl. 34, 121-135, 1990.

### Books

- G. Last und M. Penrose: "Lectures on the Poisson Process". Cambridge University Press, 2016 (to appear).

- N. Henze und G. Last: "Mathematik für Wirtschaftsingenieure und für naturwissenschaftlich-technische Studiengänge", Band 1, Vieweg Verlag, 2. Überarbeitete und erweiterte Auflage 2005.

- N. Henze und G. Last: "Mathematik für Wirtschaftsingenieure und für naturwissenschaftlich-technische Studiengänge", Band 2, Vieweg Verlag, 1. Auflage 2004.

- G. Last und A. Brandt: "Marked Point Processes on the Real Line: The Dynamic Approach", Springer-Verlag, New York, 1995.

### Talks

- "Unbiased shifts of Brownian motion and balancing random measures", 10th German Probability and Statistics Days 2012, Stochastik-Tage Mainz, 06.-09.03.2012: pdf

- "Gamma distributions in Poisson Voronoi and hyperplane tessellations", Spatial Network Models for Wireless Communications, Newton Institute Cambridge, 06.04.2010-09.04.2010: pdf

- "On the chaos expansion of Poisson functionals", 53rd Annual Meeting of the Australian Mathematical Society, Adelaide, 28.09-01.10.2009: pdf

- "On level crossings of certain Markovian jump processes", Stochastic Networks and Related Topics, Bedlewo, 27.05-01.2007: pdf

- "Distributional properties of Poisson Voronoi tessellations", Prague Stochastics 2006, 22 August, 2006: pdf

- "Stationary partitions and shift-coupling": Frankfurter Stochastik-Tage 2006, Frankfurt am Main, 14-17 March 2006: pdf

- "On Palm measures of stationary spatial point processes": Stochastic Geometry and its Applications, 3-7 October 2005, University of Bern: pdf

- "Filtering of marked point processes", National ICT Australia, Canberra, 20.07.2005: pdf

- "On Boolean models with general compact particles", Gaussian Measure and Geometric Convexity, Snowbird, 18-23 July, 2004: pdf

- "Palm measures and point stationarity", Workshop on spatial stochastic modelling, Edinburgh, 9-12 June, 2004: pdf

- "On the absence of percolation in the lilypond model", 6th German Open Conference on Probability and Stochastics, Karlsruhe, 23-26 April, 2004: pdf

Stand: 04.11.2016