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作者：Gorin, Vadim; Shkolnikov, Mykhaylo
作者单位：Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; Princeton University
摘要：We determine the operator limit for large powers of random symmetric tridiagonal matrices as the size of the matrix grows. The result provides a novel expression in terms of functionals of Brownian motions for the Laplace transform of the Airy beta process, which describes the largest eigen-values in the beta ensembles of random matrix theory. Another consequence is a Feynman-Kac formula for the stochastic Airy operator of Edelman-Sutton and Ramirez-Rider-Virag. As a side result, we find that ...
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作者：Cook, Nicholas; Goldstein, Larry; Johnson, Tobias
作者单位：Stanford University; University of Southern California
摘要：Let lambda be the second largest eigenvalue in absolute value of a uniform random d-regular graph on n vertices. It was famously conjectured by Alon and proved by Friedman that if d is fixed independent of n, then lambda = 2 root d - 1+ o(1) with high probability. In the present work, we show that lambda = O(root d) continues to hold with high probability as long as d = O(n(2/3)), making progress toward a conjecture of Vu that the bound holds for all 1 <= d <= n/2. Prior to this work the best ...
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作者：Le Page, E.; Peigne, M.; Pham, C.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study the asymptotic behaviour of the probability of non-extinction of a critical multi-type Galton-Watson process in i.i.d. random environments by using limit theorems for products of positive random matrices. Under suitable assumptions, the survival probability is proportional to 1/root n.
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作者：Feng, De-Jun; Jarvenpaa, Esa; Jarvenpaa, Maarit; Suomala, Ville
作者单位：Chinese University of Hong Kong; University of Oulu
摘要：Let M, N and K be d-dimensional Riemann manifolds. Assume that A := (A(n))(n is an element of N) is a sequence of Lebesgue measurable subsets of M satisfying a necessary density condition and x := (xn)(n is an element of N) is a sequence of independent random variables, which are distributed on K according to a measure, which is not purely singular with respect to the Riemann volume. We give a formula for the almost sure value of the Hausdorff dimension of random covering sets E(x, A) := lim s...
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作者：Berestycki, Nathanael; Lubetzky, Eyal; Peres, Yuval; Sly, Allan
作者单位：University of Cambridge; New York University; Microsoft; University of California System; University of California Berkeley
摘要：We study random walks on the giant component of the Erdos-Renyi random graph G(n, p) where p = lambda/n for lambda > 1 fixed. The mixing time from a worst starting point was shown by Fountoulakis and Reed, and independently by Benjamini, Kozma and Wormald, to have order log(2) n. We prove that starting from a uniform vertex (equivalently, from a fixed vertex conditioned to belong to the giant) both accelerates mixing to O(log n) and concentrates it (the cutoff phenomenon occurs): the typical m...
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作者：Bufetov, Alexander I.
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Kharkevich Institute for Information Transmission Problems of the RAS; HSE University (National Research University Higher School of Economics); Saint Petersburg State University
摘要：The main result of this paper is that determinantal point processes on R corresponding to projection operators with integrable kernels are quasiinvariant, in the continuous case, under the group of diffeomorphisms with compact support (Theorem 1.4); in the discrete case, under the group of all finite permutations of the phase space (Theorem 1.6). The Radon-Nikodym derivative is computed explicitly and is given by a regularized multiplicative functional. Theorem 1.4 applies, in particular, to t...
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作者：Hutchcroft, Tom
作者单位：University of Cambridge
摘要：We extend the Aldous-Broder algorithm to generate the wired uniform spanning forests (WUSFs) of infinite, transient graphs. We do this by replacing the simple random walk in the classical algorithm with Sznitman's random interlacement process. We then apply this algorithm to study the WUSF, showing that every component of the WUSF is one-ended almost surely in any graph satisfying a certain weak anchored isoperimetric condition, that the number of 'excessive ends' in the WUSF is nonrandom in a...
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作者：Panchenko, Dmitry
作者单位：University of Toronto
摘要：We study the Potts spin glass model, which generalizes the Sherrington-Kirkpatrick model to the case when spins take more than two values but their interactions are counted only if the spins are equal. We obtain the analogue of the Parisi variational formula for the free energy, with the order parameter now given by a monotone path in the set of positive-semidefinite matrices. The main idea of the paper is a novel synchronization mechanism for blocks of overlaps. This mechanism can be used to ...
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作者：Andres, Sebastian; Chiarini, Alberto; Deuschel, Jean-Dominique; Slowik, Martin
作者单位：University of Cambridge; Aix-Marseille Universite; Technical University of Berlin
摘要：We study a continuous-time random walk, X, on Z(d) in an environment of dynamic random conductances taking values in (0,infinity). We assume that the law of the conductances is ergodic with respect to space-time shifts. We prove a quenched invariance principle for the Markov process X under some moment conditions on the environment. The key result on the sublinearity of the corrector is obtained by Moser's iteration scheme.
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作者：Leao, Dorival; Ohashi, Alberto; Simas, Alexandre B.
作者单位：Universidade de Sao Paulo; Universidade Federal da Paraiba
摘要：We introduce a variational theory for processes adapted to the multidimensional Brownian motion filtration that provides a differential structure allowing to describe infinitesimal evolution of Wiener functionals at very small scales. The main novel idea is to compute the sensitivities of processes, namely derivatives of martingale components and a weak notion of infinitesimal generator, via a finite-dimensional approximation procedure based on controlled inter-arrival times and approximating ...
