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作者：Chatterjee, Sourav; Dey, Partha S.
作者单位：New York University
摘要：We prove that first-passage percolation times across thin cylinders of the form [0, n] x [-h (n) , h (n) ] (d-1) obey Gaussian central limit theorems as long as h (n) grows slower than n (1/(d+1)). It is an open question as to what is the fastest that h (n) can grow so that a Gaussian CLT still holds. Under the natural but unproven assumption about existence of fluctuation and transversal exponents, and strict convexity of the limiting shape in the direction of (1, 0, . . . , 0), we prove that...
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作者：Dumitriu, Ioana; Johnson, Tobias; Pal, Soumik; Paquette, Elliot
作者单位：University of Washington; University of Washington Seattle
摘要：Consider uniformly random permutation matrices on labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree on vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as grows to infinity, either when is kept fixed or grows slowly with . In a suitable weak convergence framework, we prove that the (finite but growing in length) seq...
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作者：Knowles, Antti; Yin, Jun
作者单位：Harvard University
摘要：We consider N x N Hermitian or symmetric random matrices with independent entries. The distribution of the (i, j)-th matrix element is given by a probability measure nu (ij) whose first two moments coincide with those of the corresponding Gaussian ensemble. We prove that the joint probability distribution of the components of eigenvectors associated with eigenvalues close to the spectral edge agrees with that of the corresponding Gaussian ensemble. For eigenvectors associated with bulk eigenva...
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作者：Bodineau, Thierry; Graham, Benjamin; Wouts, Marc
作者单位：Universite PSL; Ecole Normale Superieure (ENS); University of Warwick; Universite Paris 13
摘要：Consider Glauber dynamics for the Ising model on the hypercubic lattice with a positive magnetic field. Starting from the minus configuration, the system initially settles into a metastable state with negative magnetization. Slowly the system relaxes to a stable state with positive magnetization. Schonmann and Shlosman showed that in the two dimensional case the relaxation time is a simple function of the energy required to create a critical Wulff droplet. The dilute Ising model is obtained fr...
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作者：Olla, Stefano; Sasada, Makiko
作者单位：Universite PSL; Universite Paris-Dauphine; Keio University
摘要：We study the energy diffusion in a chain of anharmonic oscillators where the Hamiltonian dynamics is perturbed by a local energy conserving noise. We prove that under diffusive rescaling of space-time, energy fluctuations diffuse and evolve following an infinite dimensional linear stochastic differential equation driven by the linearized heat equation. We also give variational expressions for the thermal diffusivity and some upper and lower bounds.
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作者：Ichiba, Tomoyuki; Pal, Soumik; Shkolnikov, Mykhaylo
作者单位：University of California System; University of California Santa Barbara; University of Washington; University of Washington Seattle
摘要：We determine rates of convergence of rank-based interacting diffusions and semimartingale reflecting Brownian motions to equilibrium. Bounds on fluctuations of additive functionals are obtained using Transportation Cost-Information inequalities for Markov processes. We work out various applications to the rank-based abstract equity markets used in Stochastic Portfolio Theory. For example, we produce quantitative bounds, including constants, for fluctuations of market weights and occupation tim...
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作者：Kifer, Yuri
作者单位：Hebrew University of Jerusalem
摘要：In Kifer and Varadhan (Nonconventional limit theorems in discrete and continuous time via martingales, 2010) we obtained a functional central limit theorem (known also as a weak invariance principle) for sums of the form (normalized by ) where X(n), n a parts per thousand yen 0 is a sufficiently fast mixing vector process with some moment conditions and stationarity properties, F is a continuous function with polynomial growth and certain regularity properties and q (i) , i > k are positive fu...
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作者：Anshelevich, Michael
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：A fundamental result of Biane (Math Z 227:143-174, 1998) states that a process with freely independent increments has the Markov property, but that there are two kinds of free L,vy processes: the first kind has stationary increments, while the second kind has stationary transition operators. We show that a process of the first kind (with mean zero and finite variance) has the same transition operators as the free Brownian motion with appropriate initial conditions, while a process of the secon...
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作者：Curien, Nicolas; Haas, Benedicte
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Universite PSL; Universite Paris-Dauphine
摘要：We show that we can construct simultaneously all the stable trees as a nested family. More precisely, if we prove that hidden inside any -stable tree we can find a version of an -stable tree rescaled by an independent Mittag-Leffler type distribution. This tree can be explicitly constructed by a pruning procedure of the underlying stable tree or by a modification of the fragmentation associated with it. Our proofs are based on a recursive construction due to Marchal which is proved to converge...
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作者：Klopp, Frederic
作者单位：Universite Paris 13
摘要：We prove that, for a general class of random operators, the family of the unfolded eigenvalues in the localization region is asymptotically ergodic in the sense of Minami (Spectra of random operators and related topics, 2011). Minami conjectured this to be the case for discrete Anderson model in the localized regime. We also provide a local analogue of this result. From the asymptotics ergodicity, one can recover the statistics of the level spacings as well as a number of other spectral statis...
