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作者：Balazs, Marton; Busani, Ofer; Seppalainen, Timo
作者单位：University of Bristol; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider point-to-point last-passage times to every vertex in a neighbourhood of size delta N-2/3 at distance N from the starting point. The increments of the last-passage times in this neighbourhood are shown to be jointly equal to their stationary versions with high probability that depends only on delta. Through this result we show that (1) the Airy(2) process is locally close to a Brownian motion in total variation; (2) the tree of point-to-point geodesics from every vertex in a box of ...
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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); Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Aix-Marseille Universite
摘要：We obtain sharp upper and lower bounds for the downward moderate deviations of the volume of the range of a random walk in dimension five and larger. Our results encompass two regimes: a Gaussian regime for small deviations, and a stretched exponential regime for larger deviations. In the latter regime, we show that conditioned on the moderate deviations event, the walk folds a small part of its range in a ball-like subset. Also, we provide new path properties, in dimension three as well. Besi...
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作者：Bertoin, Jean
作者单位：University of Zurich
摘要：Let X-1, X-2,... be i.i.d. copies of some real random variable X. For any deterministic epsilon(2), epsilon(3),... in {0, 1}, a basic algorithm introduced by H.A. Simon yields a reinforced sequence (X) over cap (1), (X) over cap (2),... as follows. If epsilon(n) = 0, then (X) over cap (n) is a uniform random sample from (X) over cap (1), ... , (X) over cap (n-1); otherwise (X) over cap (n) is a newindependent copy of X. The purpose of this work is to compare the scaling exponent of the usual r...
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作者：Flandoli, Franco; Luo, Dejun
作者单位：Scuola Normale Superiore di Pisa; Chinese Academy of Sciences; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS
摘要：The paper is concerned with the problem of regularization by noise of 3D Navier-Stokes equations. As opposed to several attempts made with additive noise which remained inconclusive, we show here that a suitable multiplicative noise of transport type has a regularizing effect. It is proven that stochastic transport noise provides a bound on vorticity which gives well posedness, with high probability. The result holds for sufficiently large noise intensity and sufficiently high spectrum of the ...
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作者：Neuman, Eyal; Zheng, Xinghua
作者单位：Imperial College London; Hong Kong University of Science & Technology
摘要：We consider a branching random walk on Z started by n particles at the origin, where each particle disperses according to a mean-zero random walk with bounded support and reproduces with mean number of offspring 1 + theta/n. For t >= 0, we study M-nt, the rightmost position reached by the branching random walk up to generation [nt]. Under certain moment assumptions on the branching law, we prove that M-nt/root n converges weakly to the rightmost support point of the local time of the limiting ...
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作者：Michaeli, Peleg; Nachmias, Asaf; Shalev, Matan
作者单位：Tel Aviv University
摘要：We show that the diameter of a uniformly drawn spanning tree of a connected graph on n vertices which satisfies certain high-dimensionality conditions typically grows like Theta(root n). In particular this result applies to expanders, finite tori Z(m)(d) of dimension d >= 5, the hypercube {0, 1}(m), and small perturbations thereof.
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作者：Gassiat, Paul; Oberhauser, Harald; Zou, Christina Z.
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Oxford
摘要：We study the existence, optimality, and construction of non-randomised stopping times that solve the Skorokhod embedding problem (SEP) for Markov processes which satisfy a duality assumption. These stopping times are hitting times of space-time subsets, so-called Root barriers. Our main result is, besides the existence and optimality, a potential-theoretic characterisation of this Root barrier as a free boundary. If the generator of the Markov process is sufficiently regular, this reduces to a...
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作者：Dabrock, Nils; Hofmanova, Martina; Roger, Matthias
作者单位：Dortmund University of Technology; University of Bielefeld
摘要：We are concerned with a stochastic mean curvature flow of graphs over a periodic domain of any space dimension. For the first time, we are able to construct martingale solutions which satisfy the equation pointwise and not only in a generalized (distributional or viscosity) sense. Moreover, we study their large-time behavior. Our analysis is based on a viscous approximation and new global bounds, namely, an L-w,x,t(infinity) estimate for the gradient and an L-w, x,t(2) bound for the Hessian. T...
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作者：Ding, Jian; Ma, Zongming; Wu, Yihong; Xu, Jiaming
作者单位：University of Pennsylvania; Yale University; Duke University
摘要：Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erdos-Renyi graphs G(n, d/n). This can be viewed as an average-case and noisy version of the graph isomorphism problem. Under this model, the maximum likelihood estimator is equivalent to solving the intractable quadratic assignment problem. This work develops an (O) over tilde (nd(2) + n(2))-time algorit...
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作者：Yang, Fan; Yin, Jun
作者单位：University of Pennsylvania; University of California System; University of California Los Angeles
摘要：We consider a general class of symmetric or Hermitian random band matrices H = (h(xy))(x, y.)is an element of([1,N]d) in any dimension d >= 1, where the entries are independent, centered random variables with variances s(xy) = E-vertical bar hxy vertical bar 2. We assume that sxy vanishes if vertical bar x - y vertical bar exceeds the band width W, and we are interested in the mesoscopic scale with 1 << W << N. Define the generalized resolvent of H as G(H, Z) := (H - Z)(-1), where Z is a deter...
