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作者：Tao, Terence
作者单位：University of California System; University of California Los Angeles
摘要：We show that the distribution of (a suitable rescaling of) a single eigenvalue gap of a random Wigner matrix ensemble in the bulk is asymptotically given by the Gaudin-Mehta distribution, if the Wigner ensemble obeys a finite moment condition and matches moments with the GUE ensemble to fourth order. This is new even in the GUE case, as prior results establishing the Gaudin-Mehta law required either an averaging in the eigenvalue index parameter , or fixing the energy level instead of the eige...
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作者：Meister, Alexander; Reiss, Markus
作者单位：University of Rostock; Humboldt University of Berlin
摘要：Asymptotic equivalence in Le Cam's sense for nonparametric regression experiments is extended to the case of non-regular error densities, which have jump discontinuities at their endpoints. We prove asymptotic equivalence of such regression models and the observation of two independent Poisson point processes which contain the target curve as the support boundary of its intensity function. The intensity of the point processes is of order of the sample size n and involves the jump sizes as well...
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作者：DeBlassie, Dante; Smits, Robert G.
作者单位：New Mexico State University
摘要：Using a solution of a nonhomogeneous partial differential equation involving the p-Laplacian, we study the finiteness of the expected time to end the tug-of-war in a wedge.
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作者：Aidekon, E.; Berestycki, J.; Brunet, E.; Shi, Z.
作者单位：Eindhoven University of Technology; Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Cite; Sorbonne Universite
摘要：It has been conjectured since the work of Lalley and Sellke (Ann. Probab., 15, 1052-1061, 1987) that branching Brownian motion seen from its tip (e.g. from its rightmost particle) converges to an invariant point process. Very recently, it emerged that this can be proved in several different ways (see e.g. Brunet and Derrida, A branching random walk seen from the tip, 2010, Poissonian statistics in the extremal process of branching Brownian motion, 2010; Arguin et al., The extremal process of b...
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作者：Ding, Jian
作者单位：Stanford University
摘要：We study the tail behavior for the maximum of discrete Gaussian free field on a 2D box with Dirichlet boundary condition after centering by its expectation. We show that it exhibits an exponential decay for the right tail and a double exponential decay for the left tail. In particular, our result implies that the variance of the maximum is of order 1, improving an bound by Chatterjee (Chaos, concentration, and multiple valleys, 2008) and confirming a folklore conjecture. An important ingredien...
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作者：Brunick, Gerard
作者单位：University of California System; University of California Santa Barbara
摘要：We study the martingale problem associated with the operator Lu(s, x) = partial derivative(s)u(s, x) + 1/2 Sigma(d0)(i,j=1) a(ij)(s, x)partial derivative(ij)u(s, x) + Sigma(d)(i,j=1) B(ij)x(j)partial derivative(i)u(s, x), where d(0) < d. We show that the martingale problem is well-posed when the function a is continuous and strictly positive definite on R-d0 and the matrix B takes a particular lower-diagonal, block form. We then localize this result to show that the martingale problem remains ...
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作者：Ichiba, Tomoyuki; Karatzas, Ioannis; Shkolnikov, Mykhaylo
作者单位：University of California System; University of California Santa Barbara; Columbia University
摘要：We study finite and countably infinite systems of stochastic differential equations, in which the drift and diffusion coefficients of each component (particle) are determined by its rank in the vector of all components of the solution. We show that strong existence and uniqueness hold until the first time three particles collide. Motivated by this result, we improve significantly the existing conditions for the absence of such triple collisions in the case of finite-dimensional systems, and pr...
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作者：Fernholz, E. Robert; Ichiba, Tomoyuki; Karatzas, Ioannis; Prokaj, Vilmos
作者单位：University of California System; University of California Santa Barbara; Columbia University; Eotvos Lorand University; Hungarian Academy of Sciences; HUN-REN; HUN-REN Institute for Computer Science & Control
摘要：For given nonnegative constants g, h, rho, sigma with rho(2)+sigma(2) = 1 and g+h > 0, we construct a diffusion process (X-1(center dot), X-2(center dot)) with values in the plane and infinitesimal generator L=1({x1>x2})(rho(2)/2 alpha(2)/alpha x12+sigma(2)/2 alpha(2)/alpha x22-h alpha/alpha x1+g alpha/alpha x2) +1({x1>x2})(sigma(2)/2 alpha(2)/alpha x12+rho(2)/2 alpha(2)/alpha x22 + g alpha/alpha x1-h alpha/alpha x2), (0.1) and discuss its realization in terms of appropriate systems of stochas...
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作者：Benjamini, Itai; Gurel-Gurevich, Ori; Morris, Ben
作者单位：Weizmann Institute of Science; University of British Columbia; University of California System; University of California Davis
摘要：We show that the probability that a simple random walk covers a finite, bounded degree graph in linear time is exponentially small. We conjecture that the same holds for any simple graph.
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作者：Bordenave, Charles; Lelarge, Marc; Salez, Justin
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Paris Cite
摘要：Elek and Lippner (Proc. Am. Math. Soc. 138(8), 2939-2947, 2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching. We provide a characterization of the limiting parameter via a local recursion defined directly on the limit of the graph sequence. Interestingly, the recursion may admit multiple solutions, implying non-trivial long-range dependencies between the covered vertices. We over...
