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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：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：Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We prove that probability laws of certain multidimensional semimartingales which includes time-inhomogenous diffusions, under suitable assumptions, satisfy quadratic transportation cost inequality under the uniform metric. From this we derive concentration properties of Lipschitz functions of process paths that depend on the entire history. In particular, we estimate concentration of boundary local time of reflected Brownian motions on a polyhedral domain. We work out explicit applications of ...
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作者：Gravner, Janko; Holroyd, Alexander E.; Morris, Robert
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); University of California System; University of California Davis; Microsoft; University of British Columbia
摘要：Two-dimensional bootstrap percolation is a cellular automaton in which sites become 'infected' by contact with two or more already infected nearest neighbours. We consider these dynamics, which can be interpreted as a monotone version of the Ising model, on an n x n square, with sites initially infected independently with probability p. The critical probability p (c) is the smallest p for which the probability that the entire square is eventually infected exceeds 1/2. Holroyd determined the sh...
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作者：Forrester, Peter J.; Mays, Anthony
作者单位：University of Melbourne
摘要：The generalised eigenvalues for a pair of N x N matrices (X (1), X (2)) are defined as the solutions of the equation det (X (1) - lambda X (2)) = 0, or equivalently, for X (2) invertible, as the eigenvalues of . We consider Gaussian real matrices X (1), X (2), for which the generalised eigenvalues have the rotational invariance of the half-sphere, or after a fractional linear transformation, the rotational invariance of the unit disk. In these latter variables we calculate the joint eigenvalue...
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作者：Nechita, Ion; Pellegrini, Clement
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; University of Kwazulu Natal; University of Kwazulu Natal
摘要：We consider a generalized model of repeated quantum interactions, where a system H is interacting in a random way with a sequence of independent quantum systems K-n, n >= 1. Two types of randomness are studied in detail. One is provided by considering Haar-distributed unitaries to describe each interaction between H and Kn. The other involves random quantum states describing each copy K-n. In the limit of a large number of interactions, we present convergence results for the asymptotic state o...
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作者：Mijatovic, Aleksandar; Urusov, Mikhail
作者单位：Ulm University; University of Warwick
摘要：The stochastic exponential Z(t) = exp{M-t - M-0 - (1/2) < M, M >(t)} of a continuous local martingale M is itself a continuous local martingale. We give a necessary and sufficient condition for the process Z to be a true martingale in the case where M-t = integral(t)(0)b(Yu) dW(u) and Y is a one-dimensional diffusion driven by a Brownian motion W. Furthermore, we provide a necessary and sufficient condition for Z to be a uniformly integrable martingale in the same setting. These conditions are...
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作者：Du, Kai; Tang, Shanjian
作者单位：Fudan University; Fudan University; Ajou University
摘要：This paper is concerned with the strong solution to the Cauchy-Dirichlet problem for backward stochastic partial differential equations of parabolic type. Existence and uniqueness theorems are obtained, due to an application of the continuation method under fairly weak conditions on variable coefficients and C (2) domains. The problem is also considered in weighted Sobolev spaces which allow the derivatives of the solutions to blow up near the boundary. As applications, a comparison theorem is...
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作者：Chatterjee, Sourav
作者单位：New York University
摘要：We revisit strong approximation theory from a new perspective, culminating in a proof of the Komls-Major-Tusnady embedding theorem for the simple random walk. The proof is almost entirely based on a series of soft arguments and easy inequalities. The new technique, inspired by Stein's method of normal approximation, is applicable to any setting where Stein's method works. In particular, one can hope to take it beyond sums of independent random variables.
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作者：Fleming, Benjamin J.; Forrester, Peter J.; Nordenstam, Eric
作者单位：Royal Institute of Technology; University of Melbourne
摘要：The bead process is the particle system defined on parallel lines, with underlying measure giving constant weight to all configurations in which particles on neighbouring lines interlace, and zero weight otherwise. Motivated by the statistical mechanical model of the tiling of an abc-hexagon by three species of rhombi, a finitized version of the bead process is defined. The corresponding joint distribution can be realized as an eigenvalue probability density function for a sequence of random m...
