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作者：Bahadoran, C.; Mountford, T.; Ravishankar, K.; Saada, E.
作者单位：Universite Clermont Auvergne (UCA); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; New York University; NYU Shanghai; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS)
摘要：We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles. For any given environment satisfying suitable averaging properties, we establish a hydrodynamic limit given by a scalar conservation law including the domain above critical density, where the flux is shown to be constant.
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作者：Cerny, Jiri; Drewitz, Alexander
作者单位：University of Basel; University of Cologne
摘要：We consider branching random walk in spatial random branching environment (BRWRE) in dimension one, as well as related differential equations: the Fisher-KPP equation with random branching and its linearized version, the parabolic Anderson model (PAM). When the random environment is bounded, we show that after recentering and scaling, the position of the maximal particle of the BRWRE, the front of the solution of the PAM, as well as the front of the solution of the randomized Fisher-KPP equati...
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作者：Schmidt, Marius A.
作者单位：University of Basel
摘要：We give a simple proof of the theorem by Dembo, Peres, Rosen and Zeitouni (DPRZ) regarding the time Brownian motion needs to cover every epsilon ball on the two-dimensional unit torus in the epsilon SE arrow 0 limit.
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作者：Holroyd, Alexander E.; Hutchcroft, Tom; Levy, Avi
作者单位：University of Washington; University of Washington Seattle; University of Cambridge; Microsoft
摘要：We use the Mallows permutation model to construct a new family of stationary finitely dependent proper colorings of the integers. We prove that these colorings can be expressed as finitary factors of i.i.d. processes with finite mean coding radii. They are the first colorings known to have these properties. Moreover, we prove that the coding radii have exponential tails, and that the colorings can also be expressed as functions of countable-state Markov chains. We deduce analogous existence st...
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作者：Berestycki, Nathanael; Laslier, Benoit; Ray, Gourab
作者单位：University of Vienna; Universite Paris Cite; University of Victoria
摘要：We show that the winding of the branches in a uniform spanning tree on a planar graph converge in the limit of fine mesh size to a Gaussian free field. The result holds assuming only convergence of simple random walk to Brownian motion and a Russo-Seymour-Welsh type crossing estimate, thereby establishing a strong form of universality. As an application, we prove universality of the fluctuations of the height function associated to the dimer model, in several situations. The proof relies on a ...
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作者：Mareche, Laure; Martinelli, Fabio; Toninelli, Cristina
作者单位：Universite Paris Cite; Roma Tre University; Universite PSL; Universite Paris-Dauphine
摘要：Kinetically constrained models (KCM) are a class of interacting particle systems which represent a natural stochastic (and nonmonotone) counterpart of the family of cellular automata known as U-bootstrap percolation. A key issue for KCM is to identify the divergence of the characteristic time scales when the equilibrium density of empty sites, q, goes to zero. In (Ann. Probab. 47 (2019) 324-361; Comm. Math. Phys. 369 (2019) 761-809), a general scheme was devised to determine a sharp upper boun...
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作者：Devraj, Adithya; Kontoyiannis, Ioannis; Meyn, Sean
作者单位：State University System of Florida; University of Florida; University of Cambridge
摘要：For a discrete-time Markov chain X = {X (t)} evolving on R-l with transition kernel P, natural, general conditions are developed under which the following are established: (i) The transition kernel P has a purely discrete spectrum, when viewed as a linear operator on a weighted Sobolev space L-infinity(v,1) of functions with norm, parallel to f parallel to(v,1) = sup(x is an element of Rl)1/v(x)max{vertical bar f (x)vertical bar,vertical bar partial derivative(1) f (x)vertical bar, ..., a vert...
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作者：Bella, Peter; Schaffner, Mathias
作者单位：Dortmund University of Technology; Leipzig University
摘要：We consider the random conductance model in a stationary and ergodic environment. Under suitable moment conditions on the conductances and their inverse, we prove a quenched invariance principle for the random walk among the random conductances. The moment conditions improve earlier results of Andres, Deuschel and Slowik (Ann. Probab. 43 (2015) 1866-1891) and are the minimal requirement to ensure that the corrector is sublinear everywhere. The key ingredient is an essentially optimal determini...
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作者：Delarue, Francois; Lacker, Daniel; Ramanan, Kavita
作者单位：Universite Cote d'Azur; Columbia University; Brown University
摘要：We study a sequence of symmetric n-player stochastic differential games driven by both idiosyncratic and common sources of noise, in which players interact with each other through their empirical distribution. The unique Nash equilibrium empirical measure of the n-player game is known to converge, as n goes to infinity, to the unique equilibrium of an associated mean field game. Under suitable regularity conditions, in the absence of common noise, we complement this law of large numbers result...
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作者：Bender, Christian
作者单位：Saarland University
摘要：We introduce a Skorokhod type integral and prove an Ito formula for a wide class of Gaussian processes which may exhibit stochastic discontinuities. Our Ito formula unifies and extends the classical one for general (i.e., possibly discontinuous) Gaussian martingales in the sense of Ito integration and the one for stochastically continuous Gaussian non-martingales in the Skorokhod sense, which was first derived in Ales et al.
