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作者：Bordenave, Charles; Caputo, Pietro; Chafai, Djalil
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Roma Tre University
摘要：Let (X-jk)(jk >= 1) be i.i.d. nonnegative random variables with bounded density, mean m, and finite positive variance sigma(2). Let M be the n x n random Markov matrix with i.i.d. rows defined by M-jk = X-jk/( (j)1+...+X-jn). In particular, when X-11 follows an exponential law, the random matrix M belongs to the Dirichlet Markov Ensemble of random stochastic matrices. Let lambda(1),...,lambda(n) be the eigenvalues of root nM i.e. the roots in C of its characteristic polynomial. Our main result...
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作者：Addario-Berry, L.; Broutin, N.; Goldschmidt, C.
作者单位：McGill University; University of Warwick
摘要：We consider the ErdAs-R,nyi random graph G(n, p) inside the critical window, that is when p = 1/n + lambda n (-4/3), for some fixed lambda is an element of R. We prove that the sequence of connected components of G(n, p), considered as metric spaces using the graph distance rescaled by n(-1/3), converges towards a sequence of continuous compact metric spaces. The result relies on a bijection between graphs and certain marked random walks, and the theory of continuum random trees. Our result gi...
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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：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：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：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...
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作者：Klenke, Achim; Mytnik, Leonid
作者单位：Johannes Gutenberg University of Mainz; Technion Israel Institute of Technology
摘要：We construct a mutually catalytic branching process on a countable site space with infinite branching rate. The finite rate mutually catalytic model, in which the rate of branching of one population at a site is proportional to the mass of the other population at that site, was introduced by Dawson and Perkins (Ann Probab 26(3):1088-1138, 1998). We show that our model is the limit for a class of models and in particular for the Dawson-Perkins model as the rate of branching goes to infinity. Ou...
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作者：Beltran, J.; Landim, C.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Pontificia Universidad Catolica del Peru; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Let r : S x S -> R+ be the jump rates of an irreducible random walk on a finite set S, reversible with respect to some probability measure m. For alpha > 1, let g : N -> R+ be given by g(0) = 0, g(1) = 1, g(k) = (k/k - 1)(alpha), k >= 2. Consider a zero range process on S in which a particle jumps from a site x, occupied by k particles, to a site y at rate g(k)r(x, y). Let N stand for the total number of particles. In the stationary state, as N up arrow infinity, all particles but a finite num...
