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作者：Kortchemski, Igor
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：We study large random dissections of polygons. We consider random dissections of a regular polygon with n sides, which are chosen according to Boltzmann weights in the domain of attraction of a stable law of index theta is an element of (1, 2]. As n goes to infinity, we prove that these random dissections converge in distribution toward a random compact set, called the random stable lamination. If theta = 2, we recover Aldous' Brownian triangulation. However, if theta is an element of (1, 2), ...
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作者：Rhodes, Remi; Sohier, Julien; Vargas, Vincent
作者单位：Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Eindhoven University of Technology; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Ecole Normale Superieure (ENS)
摘要：In this article, we consider the continuous analog of the celebrated Mandelbrot star equation with infinitely divisible weights. Mandelbrot introduced this equation to characterize the law of multiplicative cascades. We show existence and uniqueness of measures satisfying the aforementioned continuous equation. We obtain an explicit characterization of the structure of these measures, which reflects the constraints imposed by the continuous setting. In particular, we show that the continuous e...
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作者：Glatt-Holtz, Nathan E.; Vicol, Vlad C.
作者单位：Indiana University System; Indiana University Bloomington; University of Chicago
摘要：We establish the local existence of pathwise solutions for the stochastic Euler equations in a three-dimensional bounded domain with slip boundary conditions and a suitable nonlinear multiplicative noise. In the two-dimensional case we obtain the global existence of these solutions with additive or linear-multiplicative noise. Finally, we show that, in the three-dimensional case, the addition of linear multiplicative noise provides a regularizing effect; the global existence of solutions occur...
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作者：Johnson, Tobias; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：Consider the sum of d many i.i.d. random permutation matrices on n labels along with their transposes. The resulting matrix is the adjacency matrix of a random regular (multi)-graph of degree 2d on n vertices. It is known that the distribution of smooth linear eigenvalue statistics of this matrix is given asymptotically by sums of Poisson random variables. This is in contrast with Gaussian fluctuation of similar quantities in the case of Wigner matrices. It is also known that for Wigner matric...
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作者：Moreno Flores, Gregorio R.
作者单位：Pontificia Universidad Catolica de Chile
摘要：We give a new proof of the fact that the solutions of the stochastic heat equation, started with nonnegative initial conditions, are strictly positive at positive times. The proof uses concentration of measure arguments for discrete directed polymers in Gaussian environments, originated in M. Talagrand's work on spin glasses and brought to directed polymers by Ph. Carmona and Y. Hu. We also get slightly improved bounds on the lower tail of the solutions of the stochastic heat equation started ...
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作者：Chen, Xia
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：In this paper, we study the long-term asymptotics for the quenched moment E-x exp{integral(t)(0) V (B-s) ds} consisting of a d-dimensional Brownian motion {B-s; s >= 0} and a generalized Gaussian field V. The major progress made in this paper includes: Solution to an open problem posted by Carmona and Molchanov [Probab. Theory Related Fields 102 (1995) 433-453], the quenched laws for Brownian motions in Newtonian-type potentials and in the potentials driven by white noise or by fractional whit...
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作者：Shao, Qi-Man; Zhou, Wen-Xin
作者单位：Chinese University of Hong Kong; Hong Kong University of Science & Technology
摘要：Let x(1),...,x(n) be a random sample from a p-dimensional population distribution, where p = p(n) -> infinity and log p = o(n(beta)) for some 0 < beta <= 1, and let L-n be the coherence of the sample correlation matrix. In this paper it is proved that root n/log pL(n) -> 2 in probability if and only if Ee(t0 vertical bar x11 vertical bar alpha) < infinity for some t(0) > 0, where alpha satisfies beta = alpha/(4 - alpha). Asymptotic distributions of L-n are also proved under the same sufficient...
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作者：Menz, Georg; Schlichting, Andre
作者单位：Stanford University; University of Bonn
摘要：We consider a diffusion on a potential landscape which is given by a smooth Hamiltonian H : R-n -> R in the regime of low temperature epsilon. We proof the Eyring-Kramers formula for the optimal constant in the Poincare (PI) and logarithmic Sobolev inequality (LSI) for the associated generator L = epsilon Delta - del H . del of the diffusion. The proof is based on a refinement of the two-scale approach introduced by Grunewald et al. [Ann. Inst. Henri Poincare Probab. Stat. 45 (2009) 302-351] a...
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作者：Nguyen, Hoi H.
作者单位：University System of Ohio; Ohio State University
摘要：Let X be a matrix sampled uniformly from the set of doubly stochastic matrices of size n x n. We show that the empirical spectral distribution of the normalized matrix root n(X - EX) converges almost surely to the circular law. This confirms a conjecture of Chatterjee, Diaconis and Sly.
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作者：Last, Guenter; Moerters, Peter; Thorisson, Hermann
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Bath; University of Iceland
摘要：Let B = (B-t)(t epsilon R) be a two-sided standard Brownian motion. An unbiased shift of B is a random time T, which is a measurable function of B, such that (BT+t - B-T)(t epsilon R) is a Brownian motion independent of B-T. We characterise unbiased shifts in terms of allocation rules balancing mixtures of local times of B. For any probability distribution nu on R we construct a stopping time T >= 0 with the above properties such that B-T has distribution nu. We also study moment and minimalit...
