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作者：Ameur, Yacin; Hedenmalm, Haakan; Makarov, Nikolai
作者单位：Lund University; Royal Institute of Technology; California Institute of Technology
摘要：We consider the random normal matrix ensemble associated with a potential in the plane of sufficient growth near infinity. It is known that asymptotically as the order of the random matrix increases indefinitely, the eigenvalues approach a certain equilibrium density, given in terms of Frostman's solution to the minimum energy problem of weighted logarithmic potential theory. At a finer scale, we may consider fluctuations of eigenvalues about the equilibrium. In the present paper, we give the ...
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作者：Fulman, Jason; Goldstein, Larry
作者单位：University of Southern California
摘要：With Q(q,n) the distribution of n minus the rank of a matrix chosen uniformly from the collection of all n x (n + m) matrices over the finite field F-q of size q >= 2, and Q(q) the distributional limit of Q(q,n) as n -> infinity, we apply Stein's method to prove the total variation bound 1/8q(n+m+1) <= parallel to Q(q,n) - Qq parallel to TV <= 3/q(n+m+1). In addition, we obtain similar sharp results for the rank distributions of symmetric, symmetric with zero diagonal, skew symmetric, skew cen...
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作者：Limic, Vlada; Talarczyk, Anna
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Warsaw
摘要：Consider a standard Lambda-coalescent that comes down from infinity. Such a coalescent starts from a configuration consisting of infinitely many blocks at time 0, but its number of blocks N-t is a finite random variable at each positive time t. Berestycki et al. [Ann. Probab. 38 (2010) 207-233] found the first-order approximation v for the process N at small times. This is a deterministic function satisfying N-t/v(t) -> 1 as t -> 0. The present paper reports on the first progress in the study ...
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作者：Mussel, Elchanan; Neeman, Joe
作者单位：University of California System; University of California Berkeley
摘要：We prove the first robust dimension free isoperimetric result for the standard Gaussian measure gamma n and the corresponding boundary measure gamma n(+) in R-n. The main result in the theory of Gaussian isoperimetry (proven in the 1970s by Sudakov and Tsirelson, and independently by Borell) states that if gamma n (A) = 1/2 then the surface area of A is bounded by the surface area of a half-space with the same measure, gamma n(+) (A) <= (2 pi)(-1/2). Our results imply in particular that if A s...
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作者：Angel, Omer; Ray, Gourab
作者单位：University of British Columbia; University of Cambridge
摘要：We characterize all translation invariant half-planar maps satisfying a certain natural domain Markov property. For p-angulations with p >= 3 where all faces are simple, we show that these form a one-parameter family of measures H-alpha((p)). For triangulations, we also establish existence of a phase transition which affects many properties of these maps. The critical maps are the well-known half-plane uniform infinite planar maps. The subcritical maps are identified as all possible limits of ...
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作者：Deya, Aurelien; Nualart, David; Tindel, Samy
作者单位：Universite de Lorraine; University of Kansas
摘要：This article is concerned with modulus of continuity of Brownian local times. Specifically, we focus on three closely related problems: (a) Limit theorem for a Brownian modulus of continuity involving Riesz potentials, where the limit law is an intricate Gaussian mixture. (b) Central limit theorems for the projections of L-2 modulus of continuity for a one-dimensional Brownian motion. (c) Extension of the second result to a two-dimensional Brownian motion. Our proofs rely on a combination of s...
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作者：Kaleta, Kamil; Lorinczi, Jozsef
作者单位：Wroclaw University of Science & Technology; Loughborough University
摘要：We introduce a class of Levy processes subject to specific regularity conditions, and consider their Feynman-Kac semigroups given under a Kato-class potential. Using new techniques, first we analyze the rate of decay of eigenfunctions at infinity. We prove bounds on lambda-subaveraging functions, from which we derive two-sided sharp pointwise estimates on the ground state, and obtain upper bounds on all other eigenfunctions. Next, by using these results, we analyze intrinsic ultracontractivity...
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作者：Mohammed, Salah-Eldin A.; Nilssen, Torstein K.; Proske, Frank N.
作者单位：Southern Illinois University System; Southern Illinois University; University of Oslo
摘要：In this paper, we establish the existence of a stochastic flow of Sobolev diffeomorphisms R-d (sic) x bar right arrow phi(s,t) (x) is an element of R-d, s,t is an element of R for a stochastic differential equation (SDE) of the form dX(t) = b(t, X-t)dt + dB(t), s,t is an element of R, X-s = x is an element of R-d. The above SDE is driven by a bounded measurable drift coefficient b: R x R-d -> R-d and a d-dimensional Brownian motion B. More specifically, we show that the stochastic flow phi(s,t...
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作者：Denisov, Denis; Wachtel, Vitali
作者单位：University of Manchester; University of Munich
摘要：We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk conditioned to stay in a cone. The main step in the proof consists in constructing a positive harmonic function for our random walk under minimal moment restrictions on the increments. For the proof of tail asymptotics and integral limit theorems, we use a strong approximation of random walks by Browni...
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作者：Janson, Svante; Stefansson, Sigurdur Orn
作者单位：Uppsala University; Royal Institute of Technology; Nordic Institute for Theoretical Physics; Stockholm University
摘要：We study random bipartite planar maps defined by assigning nonnegative weights to each face of a map. We prove that for certain choices of weights a unique large face, having degree proportional to the total number of edges in the maps, appears when the maps are large. It is furthermore shown that as the number of edges n of the planar maps goes to infinity, the profile of distances to a marked vertex rescaled by n(-1/2) is described by a Brownian excursion. The planar maps, with the graph met...
