Probability Theory and Related Fields

最新文章

• On properties of Parisi measures AI翻译
  作者：Auffinger, Antonio; Chen, Wei-Kuo
  作者单位：University of Chicago
  摘要：We investigate the structure of Parisi measures, the functional order parameters of mixed -spin models in mean field spin glasses. In the absence of external field, we prove that a Parisi measure satisfies the following properties. First, at all temperatures, the support of any Parisi measure contains the origin. If it contains an open interval, then the measure has a smooth density on this interval. Next, we give a criterion on temperature parameters for which a Parisi measure is neither Repl...
• Symmetric simple exclusion process with free boundaries AI翻译
  作者：De Masi, Anna; Ferrari, Pablo A.; Presutti, Errico
  作者单位：University of L'Aquila; University of Buenos Aires; Universidade de Sao Paulo; Gran Sasso Science Institute (GSSI)
  摘要：We consider the one dimensional symmetric simple exclusion process with additional births and deaths restricted to a subset of configurations where there is a leftmost hole and a rightmost particle. At a fixed rate birth of particles occur at the position of the leftmost hole and at the same rate, independently, the rightmost particle dies. We prove convergence to a hydrodynamic limit and discuss its relation with a free boundary problem.
• Persistence of integrated stable processes AI翻译
  作者：Profeta, Christophe; Simon, Thomas
  作者单位：Universite Paris Saclay; Universite de Lille; Universite Paris Saclay
  摘要：We compute the persistence exponent of the integral of a stable L,vy process in terms of its self-similarity and positivity parameters. This solves a problem raised by Shi (Lower tails of some integrated processes. In: Small deviations and related topics (problem panel 2003). Along the way, we investigate the law of the stable process evaluated at the first time its integral hits zero, when the bivariate process starts from a coordinate axis. This extends classical formul' by McKean (J Math Ky...
• On the rate of convergence in Wasserstein distance of the empirical measure AI翻译
  作者：Fournier, Nicolas; Guillin, Arnaud
  作者单位：Sorbonne Universite; Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：Let be the empirical measure associated to a -sample of a given probability distribution on . We are interested in the rate of convergence of to , when measured in the Wasserstein distance of order . We provide some satisfying non-asymptotic -bounds and concentration inequalities, for any values of and . We extend also the non asymptotic -bounds to stationary -mixing sequences, Markov chains, and to some interacting particle systems.
• Mixing time of a kinetically constrained spin model on trees: power law scaling at criticality AI翻译
  作者：Cancrini, N.; Martinelli, F.; Roberto, C.; Toninelli, C.
  作者单位：University of L'Aquila; Roma Tre University; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
  摘要：On the rooted -ary tree we consider a - kinetically constrained spin model in which the occupancy variable at each node is re-sampled with rate one from the Bernoulli(p) measure iff all its children are vacant. For this process the following picture was conjectured to hold. As long as is below the percolation threshold the process is ergodic with a finite relaxation time while, for , the process on the infinite tree is no longer ergodic and the relaxation time on a finite regular sub-tree beco...
• On the probability of staying above a wall for the -dimensional SOS model at low temperature AI翻译
  作者：Caputo, Pietro; Martinelli, Fabio; Toninelli, Fabio Lucio
  作者单位：Roma Tre University; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
  摘要：We obtain sharp asymptotics for the probability that the -dimensional discrete SOS interface at low temperature is positive in a large region. For a square region , both under the infinite volume measure and under the measure with zero boundary conditions around , this probability turns out to behave like , with the surface tension at zero tilt, also called step free energy, and L the box side. This behavior is qualitatively different from the one found for continuous height massless gradient ...
• Determinantal processes and completeness of random exponentials: the critical case AI翻译
  作者：Ghosh, Subhroshekhar
  作者单位：Princeton University
  摘要：For a locally finite point set , consider the collection of exponential functions given by . We examine the question whether spans the Hilbert space , when is random. For several point processes of interest, this belongs to a certain critical case of the corresponding question for deterministic , about which little is known. For the continuum sine kernel process, obtained as the bulk limit of GUE eigenvalues, we establish that is indeed complete almost surely. We also answer an analogous quest...
• Percolation on random triangulations and stable looptrees AI翻译
  作者：Curien, Nicolas; Kortchemski, Igor
  作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Sorbonne Universite; Universite PSL; Ecole Normale Superieure (ENS)
  摘要：We study site percolation on Angel and Schramm's uniform infinite planar triangulation. We compute several critical and near-critical exponents, and describe the scaling limit of the boundary of large percolation clusters in all regimes (subcritical, critical and supercritical). We prove in particular that the scaling limit of the boundary of large critical percolation clusters is the random stable looptree of index , which was introduced in Curien and Kortchemski (Random stable looptrees. arX...
• On the maximal displacement of critical branching random walk AI翻译
  作者：Lalley, Steven P.; Shao, Yuan
  作者单位：University of Chicago; University of Chicago
  摘要：We consider a branching random walk initiated by a single particle at location in which particles alternately reproduce according to the law of a Galton-Watson process and disperse according to the law of a driftless random walk on the integers. When the offspring distribution has mean the branching process is critical, and therefore dies out with probability . We prove that if the particle jump distribution has mean zero, positive finite variance , and finite moment, and if the offspring dist...
• KPZ relation does not hold for the level lines and flow lines of the Gaussian free field AI翻译
  作者：Aru, Juhan
  作者单位：Ecole Normale Superieure de Lyon (ENS de LYON)
  摘要：In this paper we mingle the Gaussian free field, the Schramm-Loewner evolution (SLE) and the KPZ relation in a natural way, shedding new light on all of them. In particular, we describe the quantum fractal behaviour of the level lines and the flow lines of the Gaussian free field by determining their quantum Minkowski dimensions. As a corollary we deduce that the usual KPZ relation is not satisfied. In order to determine the fractal dimensions, we have to make a technical detour: by a careful ...