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作者：Hutchcroft, Tom
作者单位：University of British Columbia
摘要：We prove that every component of the wired uniform spanning forest (WUSF) is one-ended almost surely in every transient reversible random graph, removing the bounded degree hypothesis required by earlier results. We deduce that every component of the WUSF is one-ended almost surely in every supercritical Galton Watson tree, answering a question of Benjamini, Lyons, Peres and Schramm [Ann. Probab. 29 (2001) 1-65]. Our proof introduces and exploits a family of Markov chains under which the orien...
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作者：Goldschmidt, Christina; Haas, Benedicte
作者单位：University of Oxford; Universite PSL; Universite Paris-Dauphine
摘要：We study a Markovian model for the random fragmentation of an object. At each time, the state consists of a collection of blocks. Each block waits an exponential amount of time with parameter given by its size to some power a, independently of the other blocks. Every block then splits randomly into sub-blocks whose relative sizes are distributed according to the so-called dislocation measure. We focus here on the case where alpha < 0. In this case, small blocks split intensively, and so the wh...
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作者：Quas, Anthony; Soo, Terry
作者单位：University of Victoria; University of Kansas
摘要：Sinai proved that a nonatomic ergodic measure-preserving system has any Bernoulli shift of no greater entropy as a factor. Given a Bernoulli shift, we show that any other Bernoulli shift that is of strictly less entropy and is stochastically dominated by the original measure can be obtained as a monotone factor; that is, the factor map has the property that for each point in the domain, its image under the factor map is coordinatewise smaller than or equal to the original point.
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作者：Carmona, Rene; Delarue, Francois; Lacker, Daniel
作者单位：Princeton University; Princeton University; Universite Cote d'Azur; Universite Cote d'Azur
摘要：A theory of existence and uniqueness is developed for general stochastic differential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic differential equations, and existence of weak solutions for mean field games is shown to hold under very general assumptions. Examples and counter-examples are provided to enlighten the underpinnings of the existence theory. Finally, an analog of the famous result of Yamada and...
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作者：Sheffield, Scott
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We begin by studying inventory accumulation at a LIFO (last-in-first out) retailer with two products. In the simplest version, the following occur with equal probability at each time step: first product ordered, first product produced, second product ordered, second product produced. The inventory thus evolves as a simple random walk on Z(2). In more interesting versions, a p fraction of customers orders the freshest available product regardless of type. We show that the corresponding random w...
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作者：Bandeira, Afonso S.; van Handel, Ramon
作者单位：Princeton University; Princeton University
摘要：This bound is optimal in the sense that a matching lower bound holds under mild assumptions, and the constants are sufficiently sharp that we can often capture the precise edge of the spectrum. Analogous results are obtained for rectangular matrices and for more general sub-Gaussian or heavy-tailed distributions of the entries, and we derive tail bounds in addition to bounds on the expected norm. The proofs are based on a combination of the moment method and geometric functional analysis techn...
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作者：Flandoli, Franco; Zanco, Giovanni
作者单位：University of Pisa
摘要：In this paper, a Banach space framework is introduced in order to deal with finite-dimensional path-dependent stochastic differential equations. A version of Kolmogorov backward equation is formulated and solved both in the space of LP paths and in the space of continuous paths using the associated stochastic differential equation, thus establishing a relation between path-dependent SDEs and PDEs in analogy with the classical case. Finally, it is shown how to establish a connection between suc...
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作者：Chleboun, Paul; Faggionato, Alessandra; Martinelli, Fabio
作者单位：University of Warwick; University of Warwick; Sapienza University Rome; Roma Tre University
摘要：We consider a class of kinetically constrained interacting particle systems on Z(d) which play a key role in several heuristic qualitative and quantitative approaches to describe the complex behavior of glassy dynamics. With rate one and independently among the vertices of Z(d), to each occupation variable eta(x) is an element of {0, 1} a new value is proposed by tossing a (1 - q)-coin. If a certain local constraint is satisfied by the current configuration the proposed move is accepted, other...
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作者：Leonard, Christian
作者单位：Universite Paris Saclay
摘要：This paper is about the construction of displacement interpolations of probability distributions on a discrete metric graph. Our approach is based on the approximation of any optimal transport problem whose cost function is a distance on a discrete graph by a sequence of entropy minimization problems under marginal constraints, called Schrodinger problems, which are associated with random walks. Displacement interpolations are defined as the limit of the time-marginal flows of the solutions to...
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作者：Cerf, Raphael; Gorny, Matthias
作者单位：Universite Paris Saclay
摘要：We try to design a simple model exhibiting self-organized criticality, which is amenable to a rigorous mathematical analysis. To this end, we modify the generalized Ising Curie-Weiss model by implementing an automatic control of the inverse temperature. For a class of symmetric distributions whose density satisfies some integrability conditions, we prove that the sum S-n of the random variables behaves as in the typical critical generalized Ising Curie Weiss model. The fluctuations are of orde...
