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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...
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作者：Ahlberg, Daniel
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：Large deviations in the context of first-passage percolation was first studied in the early 1980s by Grimmett and Kesten, and has since been revisited in a variety of studies. However, none of these studies provides a precise relation between the existence of moments of polynomial order and the decay of probability tails. Such a relation is derived in this paper, and is used to strengthen the conclusion of the shape theorem. In contrast to its one-dimensional counterpart-the Hsu-Robbins-Erdos ...
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作者：Petrov, Leonid
作者单位：Northeastern University; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：We study large-scale height fluctuations of random stepped surfaces corresponding to uniformly random lozenge tilings of polygons on the triangular lattice. For a class of polygons (which allows arbitrarily large number of sides), we show that these fluctuations are asymptotically governed by a Gaussian free (massless) field. This complements the similar result obtained in Kenyon [Comm. Math. Phys. 281 (2008) 675-709] about tilings of regions without frozen facets of the limit shape. In our as...
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作者：Goncalves, Patricia; Jara, Milton; Sethuraman, Sunder
作者单位：Universidade do Minho; Instituto Nacional de Matematica Pura e Aplicada (IMPA); University of Arizona
摘要：We consider a class of nearest-neighbor weakly asymmetric mass conservative particle systems evolving on Z, which includes zero-range and types of exclusion processes, starting from a perturbation of a stationary state. When the weak asymmetry is of order O (n(-gamma)) for 1/2 < gamma <= 1, we show that the scaling limit of the fluctuation field, as seen across process characteristics, is a generalized Ornstein-Uhlenbeck process. However, at the critical weak asymmetry when gamma = 1/2, we sho...
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作者：Panchenko, Dmitry
作者单位：University of Toronto
摘要：The authors of [Ann. Henri Poincare 16 (2015) 691-708] introduced a multi-species version of the Sherrington-Kirkpatrick model and suggested the analogue of the Parisi formula for the free energy. Using a variant of Guerra's replica symmetry breaking interpolation, they showed that, under certain assumption on the interactions, the formula gives an upper bound on the limit of the free energy. In this paper we prove that the bound is sharp. This is achieved by developing a new multi-species for...
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作者：Mytnik, Leonid; Wachtel, Vitali
作者单位：Technion Israel Institute of Technology; University of Munich
摘要：We show that density functions of a (alpha, 1, beta)-superprocesses are almost sure multifractal for alpha > beta + 1, beta is an element of (0, 1) and calculate the corresponding spectrum of singularities.
