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作者：Aidekon, Elie; de Raphelis, Loic
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We show that the trace of the null recurrent biased random walk on a Galton-Watson tree properly renormalized converges to the Brownian forest. Our result extends to the setting of the random walk in random environment on a Galton-Watson tree.
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作者：Baudoin, Fabrice; Wang, Jing
作者单位：University of Connecticut; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We define and study stochastic areas processes associated with Brownian motions on the complex symmetric spaces and . The characteristic functions of those processes are computed and limit theorems are obtained. In the case , we also study windings of the Brownian motion on those spaces and compute the limit distributions. For the geometry of the Hopf fibration plays a central role, whereas for it is the anti-de Sitter fibration.
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作者：Bhamidi, Shankar; Dey, Partha S.; Nobel, Andrew B.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of Illinois System; University of Illinois Urbana-Champaign
摘要：The problem of finding large average submatrices of a real-valued matrix arises in the exploratory analysis of data from a variety of disciplines, ranging from genomics to social sciences. In this paper we provide a detailed asymptotic analysis of large average submatrices of an Gaussian random matrix. The first part of the paper addresses global maxima. For fixed k we identify the average and the joint distribution of the submatrix having largest average value. As a dual result, we establish ...
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作者：Budhiraja, Amarjit; Wu, Ruoyu
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Moderate deviation principles for empirical measure processes associated with weakly interacting Markov processes are established. Two families of models are considered: the first corresponds to a system of interacting diffusions whereas the second describes a collection of pure jump Markov processes with a countable state space. For both cases the moderate deviation principle is formulated in terms of a large deviation principle (LDP), with an appropriate speed function, for suitably centered...
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作者：Subag, Eliran; Zeitouni, Ofer
摘要：Recently, sharp results concerning the critical points of the Hamiltonian of the p-spin spherical spin glass model have been obtained by means of moments computations. In particular, these moments computations allow for the evaluation of the leading term of the ground-state, i.e., of the global minimum. In this paper, we study the extremal point process of critical points-that is, the point process associated to all critical values in the vicinity of the ground-state. We show that the latter c...
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作者：Fitzner, Robert; van der Hofstad, Remco
作者单位：Eindhoven University of Technology
摘要：The lace expansion is a powerful perturbative technique to analyze the critical behavior of random spatial processes such as the self-avoiding walk, percolation and lattice trees and animals. The non-backtracking lace expansion (NoBLE) is a modification that allows us to improve its applicability in the nearest-neighbor setting on the -lattice for percolation, lattice trees and lattice animals. The NoBLE gives rise to a recursive formula that we study in this paper at a general level. We state...
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作者：Schapira, Bruno; Valesin, Daniel
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite; University of Groningen
摘要：We consider the contact process on finite and connected graphs and study the behavior of the extinction time, that is, the amount of time that it takes for the infection to disappear in the process started from full occupancy. We prove, without any restriction on the graph G, that if the infection rate is larger than the critical rate of the one-dimensional process, then the extinction time grows faster than for any constant , where |G| denotes the number of vertices of G. Also for general gra...
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作者：Asselah, Amine; Schapira, Bruno
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study the boundary of the range of simple random walk on in the transient case . We show that volumes of the range and its boundary differ mainly by a martingale. As a consequence, we obtain an upper bound on the variance of order in dimension three. We also establish a Central Limit Theorem in dimension four and larger.
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作者：Dembo, Amir; Mukherjee, Sumit
作者单位：Stanford University; Columbia University
摘要：Suppose the auto-correlations of real-valued, centered Gaussian process are non-negative and decay as for some regularly varying at infinity of order . With its primitive, we show that the persistence probabilities decay rate of is precisely of order , thereby closing the gap between the lower and upper bounds of Newell and Rosenblatt (Ann. Math. Stat. 33:1306-1313, 1962), which stood as such for over fifty years. We demonstrate its usefulness by sharpening recent results of Sakagawa (Adv. App...
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作者：Oh, Tadahiro; Tzvetkov, Nikolay
作者单位：University of Edinburgh; Heriot Watt University; University of Edinburgh; CY Cergy Paris Universite
摘要：We consider the cubic fourth order nonlinear Schrodinger equation on the circle. In particular, we prove that the mean-zero Gaussian measures on Sobolev spaces , , are quasi-invariant under the flow.
