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作者：Bernstein, Megan; Nestoridi, Evita
作者单位：University System of Georgia; Georgia Institute of Technology; Princeton University
摘要：In this paper, we use the eigenvalues of the random to random card shuffle to prove a sharp upper bound for the total variation mixing time. Combined with the lower bound due to Subag, we prove that this walk exhibits cutoff at 3/4 n log n - 1/4 n log log n with window of order n, answering a conjecture of Diaconis.
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作者：Cortines, Aser; Hartung, Lisa; Louidor, Oren
作者单位：University of Zurich; New York University; Technion Israel Institute of Technology
摘要：We study the structure of extreme level sets of a standard one-dimensional branching Brownian motion, namely the sets of particles whose height is within a fixed distance from the order of the global maximum. It is well known that such particles congregate at large times in clusters of order-one genealogical diameter around local maxima which form a Cox process in the limit. We add to these results by finding the asymptotic size of extreme level sets and the typical height of the local maxima ...
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作者：Dembo, Amir; Levit, Anna; Vadlamani, Sreekar
作者单位：Stanford University; Stanford University; University of British Columbia; Tata Institute of Fundamental Research (TIFR); TIFR Centre for Applicable Mathematics (CAM), Bengaluru
摘要：The N vertices of a quantum random graph are each a circle independently punctured at Poisson points of arrivals, with parallel connections derived through for each pair of these punctured circles by yet another independent Poisson process. Considering these graphs at their critical parameters, we show that the joint law of the rescaled by N-2/3 and ordered sizes of their connected components, converges to that of the ordered lengths of excursions above zero for a reflected Brownian motion wit...
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作者：Feng, Renjie; Adler, Robert J.
作者单位：Peking University; Technion Israel Institute of Technology
摘要：We first consider deterministic immersions of the d-dimensional sphere into high dimensional Euclidean spaces, where the immersion is via spherical harmonics of level n. The main result of the article is the, a priori unexpected, fact that there is a uniform lower bound to the critical radius of the immersions as n -> infinity. This fact has immediate implications for random spherical harmonics with fixed L-2 -norm. In particular, it leads to an exact and explicit formulae for the tail probabi...
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作者：Furlan, Marco; Gubinelli, Massimiliano
作者单位：Universite PSL; Universite Paris-Dauphine; University of Bonn
摘要：We introduce a nonlinear paracontrolled calculus and use it to renor- malise a class of singular SPDEs including certain quasilinear variants of the periodic two-dimensional parabolic Anderson model.
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作者：Dolgopyat, Dmitry; Goldsheid, Ilya
作者单位：University System of Maryland; University of Maryland College Park; University System of Maryland; University of Maryland College Park; University of London; Queen Mary University London
摘要：Environment viewed from the particle is a powerful method of analyzing random walks (RW) in random environment (RE). It is well known that in this setting the environment process is a Markov chain on the set of environments. We study the fundamental question of existence of the density of the invariant measure of this Markov chain with respect to the measure on the set of environments for RW on a strip. We first describe all positive subexponentially growing solutions of the corresponding inva...
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作者：Bertoin, Jean; Mallein, Bastien
作者单位：University of Zurich; Universite Paris 13
摘要：We call a random point measure infinitely ramified if for every n is an element of N, it has the same distribution as the nth generation of some branching random walk. On the other hand, branching Levy processes model the evolution of a population in continuous time, such that individuals move in space independently, according to some Levy process, and further beget progenies according to some Poissonian dynamics, possibly on an everywhere dense set of times. Our main result connects these two...
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作者：del Barrio, Eustasio; Loubes, Jean-Michel
作者单位：Universidad de Valladolid; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We consider the problem of optimal transportation with quadratic cost between a empirical measure and a general target probability on R-d, with d >= 1. We provide new results on the uniqueness and stability of the associated optimal transportation potentials, namely, the minimizers in the dual formulation of the optimal transportation problem. As a consequence, we show that a CLT holds for the empirical transportation cost under mild moment and smoothness requirements. The limiting distributio...
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作者：Chevyrev, Ilya; Friz, Peter K.
作者单位：University of Oxford; Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：In the spirit of Marcus canonical stochastic differential equations, we study a similar notion of rough differential equations (RDEs), notably dropping the assumption of continuity prevalent in the rough path literature. A new metric is exhibited in which the solution map is a continuous function of the driving rough path and a so-called path function, which directly models the effect of the jump on the system. In a second part, we show that general multidimensional semimartingales admit canon...
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作者：Auffinger, Antonio; Jagannath, Aukosh
作者单位：Northwestern University; Harvard University
摘要：We study the Thouless-Anderson-Palmer (TAP) equations for spin glasses on the hypercube. First, using a random, approximately ultrametric decomposition of the hypercube, we decompose the Gibbs measure, <.>(N), into a mixture of conditional laws, <.>(alpha,N). We show that the TAP equations hold for the spin at any site with respect to <.>(alpha,N) simultaneously for all alpha. This result holds for generic models provided that the Parisi measure of the model has a jump at the top of its support.
