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作者：Viklund, Fredrik Johansson
作者单位：Uppsala University
摘要：We estimate convergence rates for curves generated by Loewner's differential equation under the basic assumption that a convergence rate for the driving terms is known. An important tool is what we call the tip structure modulus, a geometric measure of regularity for Loewner curves parameterized by capacity. It is analogous to Warschawski's boundary structure modulus and closely related to annuli crossings. The main application we have in mind is that of a random discrete-model curve approachi...
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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：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：Khoshnevis, Davar; Xiao, Yimin
作者单位：Utah System of Higher Education; University of Utah; Michigan State University
摘要：Let W denote d-dimensional Brownian motion. We find an explicit formula for the essential supremum of Hausdorff dimension of W (E) boolean AND F, where E subset of (0, infinity) and F subset of R-d are arbitrary nonrandom compact sets. Our formula is related intimately to the thermal capacity of Watson [Proc. Lond. Math. Soc. (3) 37 (1978) 342-362]. We prove also that when d >= 2, our formula can be described in terms of the Hausdorff dimension of E x F, where E x F is viewed as a subspace of ...
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作者：Cass, Thomas; Hairer, Martin; Litterer, Christian; Tindel, Samy
作者单位：Imperial College London; University of Warwick; Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris; Universite de Lorraine
摘要：We consider stochastic differential equations of the form dY(t) = V(Y-t)dX(t) + V-0(Y-t)dt driven by a multi-dimensional Gaussian process. Under the assumption that the vector fields V-0 and V = (V-1,...,V-d) satisfy Hormander's bracket condition, we demonstrate that Y-t admits a smooth density for any t is an element of (0, T], provided the driving noise satisfies certain nondegeneracy assumptions. Our analysis relies on relies on an interplay of rough path theory, Malliavin calculus and the ...
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作者：Dembo, Amir; Mukherjee, Sumit
作者单位：Stanford University; Stanford University
摘要：Consider random polynomial Sigma(n)(i=0) a(i)x(i) of independent mean-zero normal coefficients a(i), whose variance is a regularly varying function (in i) of order alpha. We derive general criteria for continuity of persistence exponents for centered Gaussian processes, and use these to show that such polynomial has no roots in [0, 1] with probability n(-b alpha+o(1)), and no roots in (1, infinity) with probability n(-b0+o(1)), hence for n even, it has no real roots with probability n(-2b alph...
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作者：Le Jan, Yves; Marcus, Michael B.; Rosen, Jay
作者单位：Universite Paris Saclay; City University of New York (CUNY) System; City College of New York (CUNY); City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：A permanental field, psi = {psi(v), v is an element of V}, is a particular stochastic process indexed by a space of measures on a set S. It is determined by a kernel u(x, y), x, y is an element of S, that need not be symmetric and is allowed to be infinite on the diagonal. We show that these fields exist when u (x, y) is a potential density of a transient Markov process X in S. A permanental field psi can be realized as the limit of a renormalized sum of continuous additive functionals determi...
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作者：Mathieu, P.
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We show that the asymptotic entropy of a random walk on a nonelementary hyperbolic group, with symmetric and bounded increments, is differentiable and we identify its derivative as a correlation. We also prove similar results for the rate of escape.
