**Steven P. Lalley: Recent Papers**

- with Jayadev Athreya, Jenya Sapir, and Matthew Wroten Statistical regularities of self-intersections for geodesics on hyperbolic surfaces: local geometric properties
- with Wei Su Contact processes on random regular graphs. Annals of Applied Probability 27 (2017), no. 4, 2061-2097.
- with E. Glen Weyl Nash equilibria for a quadratic voting game.
- with Yuan Shao Maximal displacement of critical branching symmetric stable processes. Annales de l'Institut Henri Poincare Probabilites et Statistiques 52 (2016), no. 3, 1161–1177.
- with Harry Crane Exchangeable Markov processes on [k]^N with cadlag sample paths Journal of Theoretical Probability 29 (2016), no. 1, 206–230
- with Bowei Zheng Critical branching Brownian motion with killing. Electronic Journal of Probability Vol 20 (2015), Article 118
- with Piet Groeneboom and Nico Temme Chernoff's distribution and differential equations of parabolic and Airy type Journal of Mathematical Analysis and Applications vol. 423 (2015), no. 2, 1804–1824.
- with Yuan Shao On the maximal displacement of a critical branching random walk Probability Theory and Related Fields 162 (2015), no. 1-2, pp. 71–96.
- with Edwin Perkins and Xinghua Zheng A phase transition for measure-valued SIR epidemic processes Annals of Probability Vol. 42 (2014) No. 1 pp. 237-310
- Statistical regularities of self-intersection counts for geodesics on negatively curved surfaces Duke Mathematics Journal Vol. 163 (2014) No. 6 pp. 1191–1261
- with Sebastien Gouezel Random walk on a co-compact Fuchsian group Annales Scientifiques de l'Ecole Normale Superieure vol. 46 (2013) fasc. 1 pp. 1-46
- with Harry Crane Convergence rates of Markov chains on spaces of partitions Electronic Journal of Probability vol. 18 (2013) no. 61 pp. 1-23.
- with Moira Chas Self-intersections in combinatorial topology: statistical structure Inventiones Mathematicae Vol. 188 (2012), 429–463
- with Xinghua Zheng Occupation statistics of critical branching random walks Annals of Probability Vol. 39 (2011), No. 1, 327–368
- with Xinghua Zheng Spatial epidemics and local times for critical branching random walks in dimensions 2 and 3 Probability Theory and Related Fields Vol. 148 (2010), No. 3-4, 527–566
- Spatial epidemics: Critical behavior in one dimension Probability Theory and Related Fields, Vol. 144 (2009), Nos. 3--4, 429--469
- with Gregory F. Lawler and Hariharan Narayanan Geometric interpretation of half-plane capacity Electronic Communications in Probability Vol. 14 (2009), 566-571
- Random walk on a surface group: behavior of the Green's function at the spectral radius revised April 10, 2008 superceded by paper with Sebastien Gouezel
- The weak/strong survival transition on trees and nonamenable graphs Proceedings of the International Congress of Mathematicians, Madrid, Spain, 2006
- with Andrew Nobel Denoising deterministic time series Dynamics of PDE, Vol.3 (2006), No.4, 259--279
- with G. Kordzakhia Ergodicity and mixing properties of the northeast model J. Applied Probability 43 (2006) 782-792
- with R. G. Dolgoarshinnykh Critical scaling for the simple SIS stochastic epidemic J. Applied Probability 43 (2006) 892-898
- with G. Kordzakhia An oriented competition model on Z_{+}^2 Electron. Commun. Probab. 13 (2008), 548--561.
- with M. Coram Consistency of Bayes estimators of a binary regression functionAnnals of Statistics 34 (2006) 1233-1269
- with G. Kordzakhia A two-species competition model Stochastic Processes and their Applications 115 (2005) 781-796
- with Andrew Nobel Indistinguishability of absolutely continuous and singular distributions Statist. Probab. Lett. 62 (2003), no. 2, 145--154
- Strict convexity of the limit shape in first-passage percolation Electronic Communications in Probability 8 (2003) 135--141
- Algebraic systems of generating functions and return probabilities for random walks Dynamics and randomness II, 81–122, Nonlinear Phenom. Complex Systems, 10, Kluwer Acad. Publ., Dordrecht, 2004.<
- Random Walks on infinite free products and infinite algebraic systems of generating functions superceded by this paper
- with T. Sellke Anisotropic contact processes on homogeneous trees Stochastic Process. Appl. 101 (2002), no. 2, 163--183
- with T. Sellke The weak survival/strong survival phase transition for the contact process on a homogeneous tree Bulletin of the Brazilian Mathematical Society (N.S.) 33 (2002), no. 3, 341--350
- Random walks on regular languages In Algebraic Methods in Statistics and Probability (Notre Dame, IN, 2000), 201--230, Contemp. Math., 287, Amer. Math. Soc., Providence, RI, 2001.
- Percolation clusters in hyperbolic tessellations. Geometric and Functional Analysis 11 (2001) 971--1030
- Removing the Noise from Chaos Plus Noise. Nonlinear dynamics and statistics (Cambridge, 1998), 233--244
- On the rate of mixing for
*p*-shuffles. Annals of Applied Probability 10 (2000), no. 4, 1302--1321 - with T. Sellke An extension of Hawkes' theorem on the Hausdorff dimension of a Galton-Watson tree Probability Theory and Related Fields 116 Issue 1 (2000) pp 41-56.
- with I. Hueter Anisotropic branching random walks on homogeneous trees Probability Theory and Related Fields 116 Issue 1 (2000) pp 57-88.
- Beneath the noise, chaos. Annals of Statistics 27 (1999), no. 2, 461--479
- Riffle shuffles and their associated dynamical systems Journal of Theoretical Probability 12 (1999), no. 4, 903--932
- Growth profile and invariant measures for the weakly supercritical contact process on a homogeneous tree Annals of Probability 27 (1999), no. 1, 206--225
- Correction to Growth profile and invariant measures for the weakly supercritical contact process on a homogeneous tree. Annals of Probability 30 (2002) 2108-2112
- Random series in powers of algebraic integers: Hausdorff dimension of the limit distribution J. London Math. Soc. (2) 57 (1998), no. 3, 629--654.
- Percolation on Fuchsian groups Annales de l'Institut Henri Poincare Probabilites et Statistiques 34 (1998), no. 2, 151--177
- with T. Sellke Limit set of a weakly supercritical contact process on a homogeneous tree Annals of Probability 26 (1998), no. 2, 644--657
- Beta expansions with deleted digits for Pisot numbers beta Transactions of the American Mathematical Society 349 (1997), no. 11, 4355--4365
- with T. Sellke Hyperbolic branching Brownian motion Probability Theory and Related Fields 108 (1997), no. 2, 171--192

**Selected Older Papers**

- Cycle structure of riffle shuffles Annals of Probability 24 (1996) 49-73.
- Return probabilities for random walk on a half-line J. Theoret. Probab. 8 (1995) 571--599.
- Finite range random walk on free groups and homogeneous trees.Ann. Probab. 21 (1993), no. 4, 2087--2130.
- with I. Hueter Falconer's formula for the Hausdorff dimension of a self-affine set in R2. Ergodic Theory Dynam. Systems 15 (1995), no. 1, 77--97.
- with D. Gatzouras Hausdorff and box dimensions of certain self-affine fractals. Indiana Univ. Math. J. 41 (1992), no. 2, 533--568
- The packing and covering functions of some self-similar fractals. Indiana Univ. Math. J. 37 (1988), no. 3, 699--710.
- Self-intersections of closed geodesics on a negatively curved surface: statistical regularities Convergence in ergodic theory and probability (1996) 263--272
- Mostow rigidity and the Bishop-Steger dichotomy for surfaces of variable negative curvature Duke J. Math. 68 (1992) 237--269
- Renewal theorems in symbolic dynamics, with applications to geodesic flows, non-Euclidean tessellations and their fractal limits. Acta Math. 163 (1989), no. 1-2, 1--55.
- Closed geodesics in homology classes on surfaces of variable negative curvature Duke Math. J. Volume 58, Number 3 (1989), 795-821.
- Distribution of periodic orbits of symbolic and Axiom A flows. Adv. in Appl. Math. 8 (1987), no. 2, 154--193.
- with T. Sellke A conditional limit theorem for the frontier of a branching Brownian motion. Ann. Probab. 15 (1987), no. 3, 1052--1061.
- Regenerative representation for one-dimensional Gibbs states Ann. Probab. 14 (1986), no. 4, 1262--1271.
- Renewal theorem for a class of stationary sequences. Probab. Theory Relat. Fields 72 (1986), no. 2, 195--213.
- Ruelle's Perron-Frobenius theorem and the central limit theorem for additive functionals of one-dimensional Gibbs states. IMS Lecture Notes-Monograph Series, Vol. 8, "Adaptive Statistical Procedures and Related Topics" (1986)