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作者：Burdzy, Krzysztof; Chen, Zhen-Qing; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We prove that the distance between two reflected Brownian motions, driven by the same white noise, outside a sphere in a 3-dimensional flat torus does not converge to 0, a.s., if the radius of the sphere is sufficiently small, relative to the size of the torus.
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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：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：Brieussel, Jeremie
作者单位：Kyoto University
摘要：A variety of behaviors of entropy functions of random walks on finitely generated groups is presented, showing that for any 1/2 <= alpha <= beta <= 1, there is a group Gamma with measure mu equidistributed on a finite generating set such that lim inf log H-Gamma,H-mu(n)/log n = alpha, lim sup H-Gamma,H-mu(n)/log n = beta The groups involved are finitely generated subgroups of the group of automorphisms of an extended rooted tree. The return probability and the drift of a simple random walk Y-n...
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作者：Georgiou, Nicos; Seppaelaeinen, Timo
作者单位：Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：We study right tail large deviations of the logarithm of the partition function for directed lattice paths in i.i.d. random potentials. The main purpose is the derivation of explicit formulas for the 1 + 1-dimensional exactly solvable case with log-gamma distributed random weights. Along the way we establish some regularity results for this rate function for general distributions in arbitrary dimensions.
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作者：Basse-O'Connor, Andreas; Rosinski, Jan
作者单位：Aarhus University; University of Tennessee System; University of Tennessee Knoxville
摘要：Let X-n be independent random elements in the Skorohod space D([0, 1]; E) of cadlag functions taking values in a separable Banach space E. Let S-n = Sigma(n)(j=1) X-j. We show that if Sn converges in finite dimensional distributions to a cadlag process, then S-n + y(n) converges a.s. pathwise uniformly over [0, 1], for some y(n) is an element of D([0, 1]; E). This result extends the Ito-Nisio theorem to the space D([0, 1]; E), which is surprisingly lacking in the literature even for E = R. The...
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作者：Reitzner, Matthias; Schulte, Matthias
作者单位：University Osnabruck; Helmholtz Association; Karlsruhe Institute of Technology
摘要：A U-statistic of a Poisson point process is defined as the sum Sigma f(x(1),...,x(k)) over all (possibly infinitely many) k-tuples of distinct points of the point process. Using the Malliavin calculus, the Wiener-Ito chaos expansion of such a functional is computed and used to derive a formula for the variance. Central limit theorems for U-statistics of Poisson point processes are shown, with explicit bounds for the Wasserstein distance to a Gaussian random variable. As applications, the inter...
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作者：Auffinger, Antonio; Ben Arous, Gerard
作者单位：University of Chicago; New York University
摘要：We analyze the landscape of general smooth Gaussian functions on the sphere in dimension N, when N is large. We give an explicit formula for the asymptotic complexity of the mean number of critical points of finite and diverging index at any level of energy and for the mean Euler characteristic of level sets. We then find two possible scenarios for the bottom landscape, one that has a layered structure of critical values and a strong correlation between indexes and critical values and another ...
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作者：Drapeau, Samuel; Heyne, Gregor; Kupper, Michael
作者单位：Humboldt University of Berlin
摘要：We study the nonlinear operator of mapping the terminal value xi to the corresponding minimal supersolution of a backward stochastic differential equation with the generator being monotone in y, convex in z, jointly lower semicontinuous and bounded below by an affine function of the control variable z. We show existence, uniqueness, monotone convergence, Fatou's lemma and lower semicontinuity of this operator. We provide a comparison principle for minimal supersolutions of BSDEs.
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作者：Dembo, Amir; Montanari, Andrea; Sun, Nike
作者单位：Stanford University; Stanford University; Stanford University
摘要：We consider homogeneous factor models on uniformly sparse graph sequences converging locally to a (unimodular) random tree T, and study the existence of the free energy density phi, the limit of the log-partition function divided by the number of vertices n as n tends to infinity. We provide a new interpolation scheme and use it to prove existence of, and to explicitly compute, the quantity phi subject to uniqueness of a relevant Gibbs measure for the factor model on T. By way of example we co...
