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作者：Feray, Valentin; Meliot, Pierre-Loic
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux; Universite Gustave-Eiffel
摘要：In this paper, we are interested in the asymptotic size of the rows and columns of a random Young diagram under a natural deformation of the Plancherel measure coming from Hecke algebras. The first lines of such diagrams are typically of order n, so it does not fit in the context of the work of Biane (Int Math Res Notices 4:179-192, 2001) and Aeniady (Probab. Theory Relat Fields 136:263-297, 2006). Using the theory of polynomial functions on Young diagrams of Kerov and Olshanski, we are able t...
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作者：Faraud, Gabriel; Hu, Yueyun; Shi, Zhan
作者单位：Universite Paris 13; Sorbonne Universite
摘要：We are interested in the biased random walk on a supercritical Galton-Watson tree in the sense of Lyons (Ann. Probab. 18:931-958, 1990) and Lyons, Pemantle and Peres (Probab. Theory Relat. Fields 106:249-264, 1996), and study a phenomenon of slow movement. In order to observe such a slow movement, the bias needs to be random; the resulting random walk is then a tree-valued random walk in random environment. We investigate the recurrent case, and prove, under suitable general integrability assu...
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作者：Bieniek, Mariusz; Burdzy, Krzysztof; Finch, Sam
作者单位：University of Washington; University of Washington Seattle; Maria Curie-Sklodowska University; Aarhus University
摘要：We consider a branching particle model in which particles move inside a Euclidean domain according to the following rules. The particles move as independent Brownian motions until one of them hits the boundary. This particle is killed but another randomly chosen particle branches into two particles, to keep the population size constant. We prove that the particle population does not approach the boundary simultaneously in a finite time in some Lipschitz domains. This is used to prove a limit t...
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作者：Jiang, Tiefeng
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：For each n a parts per thousand yen 2, let A (n) = (xi (ij) ) be an n x n symmetric matrix with diagonal entries equal to zero and the entries in the upper triangular part being independent with mean mu (n) and standard deviation sigma (n) . The Laplacian matrix is defined by . In this paper, we obtain the laws of large numbers for lambda (n-k) (Delta (n) ), the (k + 1)-th smallest eigenvalue of Delta (n) , through the study of the order statistics of weakly dependent random variables. Under c...
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作者：Kerkyacharian, Gerard; Nickl, Richard; Picard, Dominique
作者单位：University of Cambridge; Universite Paris Cite; Sorbonne Universite
摘要：Let X (1), . . . , X (n) be a random sample from some unknown probability density f defined on a compact homogeneous manifold M of dimension d a parts per thousand yen 1. Consider a 'needlet frame' describing a localised projection onto the space of eigenfunctions of the Laplace operator on M with corresponding eigenvalues less than 2(2j) , as constructed in Geller and Pesenson (J Geom Anal 2011). We prove non-asymptotic concentration inequalities for the uniform deviations of the linear needl...
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作者：Bekjan, Turdebek N.; Chen, Zeqian
作者单位：Chinese Academy of Sciences; Innovation Academy for Precision Measurement Science & Technology, CAS; Xinjiang University
摘要：This paper is devoted to the study of phi-moment inequalities for noncommutative martingales. In particular, we prove the noncommutative phi-moment analogues of martingale transformations, Stein's inequalities, Khintchine's inequalities for Rademacher's random variables, and Burkholder-Gundy's inequalities. The key ingredient is a noncommutative version of Marcinkiewicz type interpolation theorem for Orlicz spaces which we establish in this paper.
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作者：Becker, Mathias; Koenig, Wolfgang
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technical University of Berlin
摘要：Fix p > 1, not necessarily integer, with p(d - 2) < d. We study the p-fold self-intersection local time of a simple random walk on the lattice up to time t. This is the p-norm of the vector of the walker's local times, a (t) . We derive precise logarithmic asymptotics of the expectation of exp{theta (t) ||a (t) || (p) } for scales theta (t) > 0 that are bounded from above, possibly tending to zero. The speed is identified in terms of mixed powers of t and theta (t) , and the precise rate is ch...
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作者：Erdos, Laszlo; Yau, Horng-Tzer; Yin, Jun
作者单位：Harvard University; University of Munich
摘要：Consider N x N Hermitian or symmetric random matrices H where the distribution of the (i, j) matrix element is given by a probability measure nu (ij) with a subexponential decay. Let be the variance for the probability measure nu (ij) with the normalization property that for all j. Under essentially the only condition that for some constant c > 0, we prove that, in the limit N -> a, the eigenvalue spacing statistics of H in the bulk of the spectrum coincide with those of the Gaussian unitary o...
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作者：Benaych-Georges, F.; Guionnet, A.; Maida, M.
作者单位：Sorbonne Universite; Universite Paris Cite; Ecole Normale Superieure de Lyon (ENS de LYON); Universite Paris Saclay
摘要：Consider a real diagonal deterministic matrix X (n) of size n with spectral measure converging to a compactly supported probability measure. We perturb this matrix by adding a random finite rank matrix, with delocalized eigenvectors. We show that the joint law of the extreme eigenvalues of the perturbed model satisfies a large deviation principle in the scale n, with a good rate function given by a variational formula. We tackle both cases when the extreme eigenvalues of X (n) converge to the ...
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作者：Crawford, Nicholas; Sly, Allan
作者单位：Technion Israel Institute of Technology; Microsoft
摘要：In this paper, we derive upper bounds for the heat kernel of the simple random walk on the infinite cluster of a supercritical long range percolation process. For any d a parts per thousand yen 1 and for any exponent giving the rate of decay of the percolation process, we show that the return probability decays like up to logarithmic corrections, where t denotes the time the walk is run. Our methods also yield generalized bounds on the spectral gap of the dynamics and on the diameter of the la...
