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作者：Fribergh, Alexander
作者单位：Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse
摘要：We study the biased random walk in positive random conductances on Z(d). This walk is transient in the direction of the bias. Our main result is that the random walk is ballistic if, and only if, the conductances have finite mean. Moreover, in the sub-ballistic regime we find the polynomial order of the distance moved by the particle. This extends results obtained by Shen [Ann. Appl. Probab. 12 (2002) 477-510], who proved positivity of the speed in the uniformly elliptic setting.
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作者：Hammond, Alan
作者单位：University of Oxford
摘要：We consider a random walk on a supercritical Galton-Watson tree with leaves, where the transition probabilities of the walk are determined by biases that are randomly assigned to the edges of the tree. The biases are chosen independently on distinct edges, each one according to a given law that satisfies a logarithmic nonlattice condition. We determine the condition under which the walk is sub-ballistic, and, in the sub-ballistic regime, we find a formula for the exponent gamma epsilon (0, 1) ...
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作者：Bednorz, Witold
作者单位：University of Warsaw
摘要：In this paper we prove the complete characterization of a.s. convergence of orthogonal series in terms of existence of a majorizing measure. It means that for a given (a(n))(n=1)(infinity), a(n) > 0, series Sigma(infinity)(n=1) a(n)phi(n) is a.e. convergent for each orthonormal sequence (phi(n))(n=1)(infinity) if and only if there exists a measure m on T = {0} boolean OR {Sigma(m)(n=1) a(n)(2), m >= 1} such that sup(t is an element of T)integral(root D(T))(0) (m(B(t, r(2))))(-1/2) dr < infinit...
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作者：Junge, Marius; Zeng, Qiang
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：In this paper we extend the Bernstein, Prohorov and Bennett inequalities to the noncommutative setting. In addition we provide an improved version of the noncommutative Rosenthal inequality, essentially due to Nagaev, Pinelis and Pinelis, Utev for commutative random variables. We also present new best constants in Rosenthal's inequality. Applying these results to random Fourier projections, we recover and elaborate on fundamental results from compressed sensing, due to Candes, Romberg and Tao.
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作者：Menz, Georg; Otto, Felix
作者单位：Max Planck Society
摘要：We consider a noninteracting unbounded spin system with conservation of the mean spin. We derive a uniform logarithmic Sobolev inequality (LSI) provided the single-site potential is a bounded perturbation of a strictly convex function. The scaling of the LSI constant is optimal in the system size. The argument adapts the two-scale approach of Grunewald, Villani, Westdickenberg and the second author from the quadratic to the general case. Using an asymmetric Brascamp Lieb-type inequality for co...
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作者：Deligiannidis, George; Utev, Sergey
作者单位：University of Oxford; University of Nottingham
摘要：Let X-1, X-2, ... be a centred sequence of weakly stationary random variables with spectral measure F and partial sums S-n = X-1 + ... + X-n. We show that var(S-n) is regularly varying of index gamma at infinity, if and only if G(x) := integral(x)(-x) F(dx) is regularly varying of index 2 - gamma at the origin (0 < gamma < 2).
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作者：Grimmett, Geoffrey R.; Manolescu, Joan
作者单位：University of Cambridge
摘要：All (in)homogeneous bond percolation models on the square, triangular, and hexagonal lattices belong to the same universality class, in the sense that they have identical critical exponents at the critical point (assuming the exponents exist). This is proved using the star triangle transformation and the box-crossing property. The exponents in question are the one-arm exponent rho, the 2j-alternating-arms exponents rho(2j) for j >= 1, the volume exponent delta, and the connectivity exponent et...
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作者：Aidekon, Elie
作者单位：Eindhoven University of Technology
摘要：We consider the minimum of a super-critical branching random walk. Addario-Berry and Reed [Ann. Probab. 37 (2009) 1041-1079] proved the tightness of the minimum centered around its mean value. We show that a convergence in law holds, giving the analog of a well-known result of Bramson [Mem. Amer Math. Soc. 44 (1983) iv+190] in the case of the branching Brownian motion.
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作者：Brzezniak, Zdzislaw; Ondrejat, Martin
作者单位：University of York - UK; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
摘要：Let M be a compact Riemannian homogeneous space (e.g., a Euclidean sphere). We prove existence of a global weak solution of the stochastic wave equation D-t partial derivative(t)u = Sigma(d)(k=1) D-xk partial derivative(xk)u+f(u)(Du)+g(u)(D-u)(W) over dot in any dimension d >= 1, where f and g are continuous multilinear maps, and W is a spatially homogeneous Wiener process on R-d with finite spectral measure. A nonstandard method of constructing weak solutions of SPDEs, that does not rely on m...
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作者：Corwin, Ivan; Quastel, Jeremy
作者单位：New York University; University of Toronto
摘要：We consider the weakly asymmetric limit of simple exclusion process with drift to the left, starting from step Bernoulli initial data with rho(-) < rho(+) so that macroscopically one has a rarefaction fan. We study the fluctuations of the process observed along slopes in the fan, which are given by the Hopf-Cole solution of the Kardar-Parisi-Zhang (KPZ) equation, with appropriate initial data. For slopes strictly inside the fan, the initial data is a Dirac delta function and the one point dist...
