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作者：Holroyd, Alexander E.; Lyons, Russell; Soo, Terry
作者单位：Microsoft; Indiana University System; Indiana University Bloomington; University of Victoria
摘要：Given a homogeneous Poisson process on R-d with intensity lambda, we prove that it is possible to partition the points into two sets, as a deterministic function of the process, and in an isometry-equivariant way, so that each set of points forms a homogeneous Poisson process, with any given pair of intensities summing to lambda. In particular, this answers a question of Ball [Electron. Commun. Probab. 10 (2005) 60-69], who proved that in d = 1, the Poisson points may be similarly partitioned ...
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作者：Rohde, Steffen
作者单位：University of Washington; University of Washington Seattle
摘要：In this note, I will describe some highlights of Oded Schramm's work in circle packings and the Koebe conjecture, as well as on SLE.
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作者：Bordenave, Charles; Caputo, Pietro; Chafai, Djalil
作者单位：Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Roma Tre University; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：We consider the random reversible Markov kernel K obtained by assigning i.i.d. nonnegative weights to the edges of the complete graph over n vertices and normalizing by the corresponding row sum. The weights are assumed to be in the domain of attraction of an a-stable law, alpha is an element of (0, 2). When 1 <= alpha < 2, we show that for a suitable regularly varying sequence kappa(n) of index 1 - 1/alpha, the limiting spectral distribution mu(alpha) of kappa(n) K coincides with the one of t...
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作者：Liggett, Thomas M.
作者单位：University of California System; University of California Los Angeles
摘要：Interacting particle systems and percolation have been among the most active areas of probability theory over the past half century. Ted Harris played an important role in the early development of both fields. This paper is a bird's eye view of his work in these fields, and of its impact on later research in probability theory and mathematical physics.
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作者：Ben Arous, Gerard; Corwin, Ivan
作者单位：New York University
摘要：We consider the family of two-sided Bernoulli initial conditions for TASEP which, as the left and right densities (rho-, rho+) are varied, give rise to shock waves and rarefaction fans-the two phenomena which are typical to TASEP. We provide a proof of Conjecture 7.1 of [Progr. Probab. 51 (2002) 185-204] which characterizes the order of and scaling functions for the fluctuations of the height function of two-sided TASEP in terms of the two densities rho-, rho+ and the speed y around which the ...
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作者：Jara, Milton; Landim, Claudio; Teixeira, Augusto
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rouen Normandie; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：In this paper, we study Bouchaud's trap model on the discrete d-dimensional torus T-n(d) = (Z/nZ)(d). In this process, a particle performs a symmetric simple random walk, which waits at the site x is an element of T-n(d), an exponential time with mean xi x, where {xi x, x is an element of T-n(d)} is a realization of an i.i.d. sequence of positive random variables with an alpha-stable law. Intuitively speaking, the value of xi x gives the depth of the trap at x. In dimension d = 1, we prove tha...
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作者：Nualart, David; Tindel, Samy
作者单位：University of Kansas; Universite de Lorraine
摘要：This note is devoted to construct a rough path above a multidimensional fractional Brownian motion B with any Hurst parameter H is an element of (0, 1), by means of its representation as a Volterra Gaussian process. This approach yields some algebraic and computational simplifications with respect to [Stochastic Process. Appl. 120 (2010) 1444-1472], where the construction of a rough path over B was first introduced.
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作者：Chen, Xia; Li, Wenbo V.; Rosinski, Jan; Shao, Qi-Man
作者单位：University of Tennessee System; University of Tennessee Knoxville; University of Delaware; Hong Kong University of Science & Technology
摘要：In this paper, we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann Liouville processes. We also show that a fractional Brownian motion and the related Riemann-Liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times. As a consequence of our large deviation estimates, we derive laws of iterated logarithm for the corresponding local times...
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作者：Lacoin, Hubert
作者单位：Roma Tre University
摘要：In this paper, we study a model of a Brownian polymer in R+ x R-d, introduced by Rovira and Tindel [J. Fund. Anal. 222 (2005) 178-201]. Our investigation focuses mainly on the effect of strong spatial correlation in the environment in that model in terms of free energy, fluctuation exponent and volume exponent. In particular, we prove that under some assumptions, very strong disorder and superdiffusivity hold at all temperatures when d >= 3 and provide a novel approach to Petermann's superdiff...
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作者：Bogachev, Leonid V.; Zarbaliev, Sakhavat M.
作者单位：University of Leeds; Russian Academy of Sciences; Institute of Earthquake Prediction Theory & Mathematical Geophysics
摘要：Let Pi(n) be the set of convex polygonal lines Gamma with vertices on Z(+)(2) and fixed endpoints 0 = (0, 0) and n = (n(1), n(2)). We are concerned with the limit shape, as n -> 8, of typical Gamma is an element of Pi(n) with respect to a parametric family of probability measures {P-n(r), 0 < r < infinity} on Pi(n), including the uniform distribution (r = 1) for which the limit shape was found in the early 1990s independently by A. M. Vershik, I. Barany and Ya. G. Sinai. We show that, in fact,...
