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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...
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作者：Tassion, Vincent
作者单位：University of Geneva
摘要：We prove that the standard Russo-Seymour-Welsh theory is valid for Voronoi percolation. This implies that at criticality the crossing probabilities for rectangles are bounded by constants depending only on their aspect ratio. This result has many consequences, such as the polynomial decay of the one arm event at criticality.
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作者：Puhalskii, Anatolii A.
摘要：We consider two Ito equations that evolve on different time scales. The equations are fully coupled in the sense that all of the coefficients may depend on both the slow and the fast variables and the diffusion terms may be correlated. The diffusion term in the slow process is small. A large deviation principle is obtained for the joint distribution of the slow process and of the empirical process of the fast variable. By projecting on the slow and fast variables, we arrive at new results on l...
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作者：Duminil-Copin, Hugo; van Enter, Aernout
作者单位：University of Geneva; University of Groningen
