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作者：Angel, Omer; Ray, Gourab
作者单位：University of British Columbia; University of Cambridge
摘要：We characterize all translation invariant half-planar maps satisfying a certain natural domain Markov property. For p-angulations with p >= 3 where all faces are simple, we show that these form a one-parameter family of measures H-alpha((p)). For triangulations, we also establish existence of a phase transition which affects many properties of these maps. The critical maps are the well-known half-plane uniform infinite planar maps. The subcritical maps are identified as all possible limits of ...
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作者：Ambrsio, Luigi; Gigli, Nicola; Savare, Giuseppe
作者单位：Scuola Normale Superiore di Pisa; Universite Paris Cite; Sorbonne Universite; University of Pavia
摘要：The aim of the present paper is to bridge the gap between the Bakry-Emery and the Lott-Sturm-Villani approaches to provide synthetic and abstract notions of lower Ricci curvature bounds. We start from a strongly local Dirichlet form epsilon admitting a Carre du champ F in a Polish measure space (X, m) and a canonical distance de that induces the original topology of X. We first characterize the distinguished class of Riemannian Energy measure spaces, where epsilon coincides with the Cheeger en...
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作者：Owada, Takashi; Samorodnitsky, Gennady
作者单位：Cornell University; Cornell University
摘要：We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying Levy measures. The limit process is a new class of symmetric stable self-similar processes with stationary increments that coincides on a part of its parameter space with a previously described process. The normalizing sequence and the limiting process are determined by the ergodic-theoretical properties of the flow underlying the i...
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作者：Gorin, Vadim; Panova, Greta
作者单位：Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; University of Pennsylvania
摘要：We develop a new method for studying the asymptotics of symmetric polynomials of representation-theoretic origin as the number of variables tends to infinity. Several applications of our method are presented: We prove a number of theorems concerning characters of infinite-dimensional unitary group and their q-deformations. We study the behavior of uniformly random lozenge tilings of large polygonal domains and find the GUE-eigenvalues distribution in the limit. We also investigate similar beha...
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作者：Perkowski, Nicolas; Ruf, Johannes
作者单位：Universite PSL; Universite Paris-Dauphine; University of London; University College London
摘要：Certain countably and finitely additive measures can be associated to a given nonnegative supermartingale. Under weak assumptions on the underlying probability space, existence and (non)uniqueness results for such measures are proven.
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作者：Deya, Aurelien; Nualart, David; Tindel, Samy
作者单位：Universite de Lorraine; University of Kansas
摘要：This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on three closely related problems: (a) Limit theorem for a Brownian modulus of continuity involving Riesz potentials, where the limit law is an intricate Gaussian mixture. (b) Central limit theorems for the projections of L-2 modulus of continuity for a one-dimensional Brownian motion. (c) Extension of the second result to a two-dimensional Brownian motion. Our proofs rely on a combination of s...
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作者：Kargin, V.
作者单位：University of Cambridge
摘要：This paper is about the relation of random matrix theory and the subordination phenomenon in complex analysis. We find that the resolvent of the sum of two random matrices is approximately subordinated to the resolvents of the original matrices. We estimate the error terms in this relation and in the subordination relation for the traces of the resolvents. This allows us to prove a local limit law for eigenvalues and a delocalization result for eigenvectors of the sum of two random matrices. I...
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作者：Kaleta, Kamil; Lorinczi, Jozsef
作者单位：Wroclaw University of Science & Technology; Loughborough University
摘要：We introduce a class of Levy processes subject to specific regularity conditions, and consider their Feynman-Kac semigroups given under a Kato-class potential. Using new techniques, first we analyze the rate of decay of eigenfunctions at infinity. We prove bounds on lambda-subaveraging functions, from which we derive two-sided sharp pointwise estimates on the ground state, and obtain upper bounds on all other eigenfunctions. Next, by using these results, we analyze intrinsic ultracontractivity...
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作者：Mohammed, Salah-Eldin A.; Nilssen, Torstein K.; Proske, Frank N.
作者单位：Southern Illinois University System; Southern Illinois University; University of Oslo
摘要：In this paper, we establish the existence of a stochastic flow of Sobolev diffeomorphisms R-d (sic) x bar right arrow phi(s,t) (x) is an element of R-d, s,t is an element of R for a stochastic differential equation (SDE) of the form dX(t) = b(t, X-t)dt + dB(t), s,t is an element of R, X-s = x is an element of R-d. The above SDE is driven by a bounded measurable drift coefficient b: R x R-d -> R-d and a d-dimensional Brownian motion B. More specifically, we show that the stochastic flow phi(s,t...
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作者：Carmona, Rene; Delarue, Francois
作者单位：Princeton University; Universite Cote d'Azur
摘要：The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of McKean Vlasov type. Motivated by the recent interest in mean-field games, we highlight the connection and the differences between the two sets of problems. We prove a new version of the stochastic maximum principle and give sufficient conditions for existence of an optimal control. We also provide examples for which our sufficient conditions for existenc...
