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作者：Limic, Vlada; Talarczyk, Anna
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Warsaw
摘要：Consider a standard Lambda-coalescent that comes down from infinity. Such a coalescent starts from a configuration consisting of infinitely many blocks at time 0, but its number of blocks N-t is a finite random variable at each positive time t. Berestycki et al. [Ann. Probab. 38 (2010) 207-233] found the first-order approximation v for the process N at small times. This is a deterministic function satisfying N-t/v(t) -> 1 as t -> 0. The present paper reports on the first progress in the study ...
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作者：Lam, Thomas
作者单位：University of Michigan System; University of Michigan
摘要：Let W be a finite Weyl group and (W) over cap be the corresponding affine Weyl group. We show that a large element in (W) over cap, randomly generated by (reduced) multiplication by simple generators, almost surely has one of vertical bar W vertical bar-specific shapes. Equivalently, a reduced random walk in the regions of the affine Coxeter arrangement asymptotically approaches one of vertical bar W vertical bar-many directions. The coordinates of this direction, together with the probabiliti...
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作者：Mussel, Elchanan; Neeman, Joe
作者单位：University of California System; University of California Berkeley
摘要：We prove the first robust dimension free isoperimetric result for the standard Gaussian measure gamma n and the corresponding boundary measure gamma n(+) in R-n. The main result in the theory of Gaussian isoperimetry (proven in the 1970s by Sudakov and Tsirelson, and independently by Borell) states that if gamma n (A) = 1/2 then the surface area of A is bounded by the surface area of a half-space with the same measure, gamma n(+) (A) <= (2 pi)(-1/2). Our results imply in particular that if A s...
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作者：Broutin, Nicolas; Sulzbach, Henning
作者单位：McGill University
摘要：In the recursive lamination of the disk, one tries to add chords one after another at random; a chord is kept and inserted if it does not intersect any of the previously inserted ones. Curien and Le Gall [Ann. Probab. 39 (2011) 2224-2270] have proved that the set of chords converges to a limit triangulation of the disk encoded by a continuous process M. Based on a new approach resembling ideas from the so-called contraction method in function spaces, we prove that, when properly rescaled, the ...
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作者：Hammond, Alan; Pete, Gabor; Schramm, Oded
作者单位：University of Oxford; Budapest University of Technology & Economics
摘要：In dynamical critical site percolation on the triangular lattice or bond percolation on Z(2), we define and study a local time measure on the exceptional times at which the origin is in an infinite cluster. We show that at a typical time with respect to this measure, the percolation configuration has the law of Kesten's incipient infinite cluster. In the most technical result of this paper, we show that, on the other hand, at the first exceptional time, the law of the configuration is differen...
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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.
