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作者：Poplavskyi, Mihail; Tribe, Roger; Zaboronski, Oleg
作者单位：University of Warwick
摘要：Let root N + lambda(maX), be the largest real eigenvalue of a random N x N matrix with independent N(0, 1) entries (the real Ginibre matrix). We study the large deviations behaviour of the limiting N -> infinity distribution P[lambda(max) < t] of the shifted maximal real eigenvalue, lambda(max). In particular, we prove that the right tail of this distribution is Gaussian: for t > 0, P[lambda(max) < t] = 1 - 1/4 erfc(t) + O (e(-2t2)). This is a rigorous confirmation of the corresponding result ...
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作者：Li, Yao; Young, Lai-Sang
作者单位：University of Massachusetts System; University of Massachusetts Amherst; New York University
摘要：We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent with analogous mechanical models. Our main result is that the rate of convergence to equilibrium for such a system is similar to t(-2), more precisely it is faster than a constant times t(-2+epsilon) for any epsilon > 0. A discussion of exponential vs. poly...
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作者：Aletti, Giacomo; Crimaldi, Irene; Ghiglietti, Andrea
作者单位：University of Milan; IMT School for Advanced Studies Lucca
摘要：Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon that could be roughly defined as the tendency of different components to adopt a common behavior. We continue the study of a model of interacting stochastic processes with reinforcement that recently has been introduced in [Crimaldi et al. (2016)]. Generally speaking, by reinforcement we mean any mech...
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作者：Bhattacharya, Bhaswar B.; Diaconis, Persi; Mukherjeet, Sumit
作者单位：University of Pennsylvania; Stanford University; Columbia University
摘要：This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. These can be seen as generalizations of the birthday problem (what is the chance that there are two friends with the same birthday?). It is shown that if the number of colors grows to infinity, the asymptotic distribution is either a Poisson mixture or a Normal depending solely on the limiting behavior of the ratio of the number of edges in the graph and the number of co...
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作者：Burdzy, Krzysztof; Tadic, Tvrtko
作者单位：University of Washington; University of Washington Seattle; Microsoft; University of Zagreb
摘要：We consider two-dimensional and three-dimensional semi-infinite tubes made of Lambertian material, so that the distribution of the direction of a reflected light ray has the density proportional to the cosine of the angle with the normal vector. If the light source is far away from the opening of the tube then the exiting rays are (approximately) collimated in two dimensions but are not collimated in three dimensions. An observer looking into the three-dimensional tube will see infinitely brig...
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作者：Chen, Zhen-Qing; Fan, Wai-Tong (Louis)
作者单位：University of Washington; University of Washington Seattle; University of Wisconsin System; University of Wisconsin Madison
摘要：A new non-conservative stochastic reaction diffusion system in which two families of random walks in two adjacent domains interact near the interface is introduced and studied in this paper. Such a system can be used to model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition. We show that in the macroscopic limit, the particle densities converge to the solution of a coupled nonlinear heat equations. For this, w...
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作者：Helmes, Kurt L.; Stockbridge, Richard H.; Zhu, Chao
作者单位：Humboldt University of Berlin; University of Wisconsin System; University of Wisconsin Milwaukee
摘要：This paper establishes conditions for optimality of an (s, S) ordering policy for the minimization of the long-term average cost of one-dimensional diffusion inventory models. The class of such models under consideration have general drift and diffusion coefficients and boundary points that are consistent with the notion that demand should tend to reduce the inventory level. Characterization of the cost of a general (s, S) policy as a function F of two variables naturally leads to a nonlinear ...
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作者：Ball, Frank; Neal, Peter
作者单位：University of Nottingham; Lancaster University
摘要：For a supercritical configuration model random graph, it is well known that, subject to mild conditions, there exists a unique giant component, whose size R-n is O (n), where n is the total number of vertices in the random graph. Moreover, there exists 0 < rho <= 1 such that R-n/n ->(p) rho as n -> infinity. We show that for a sequence of well behaved configuration model random graphs with a deterministic degree sequence satisfying 0 < rho < 1; there exists sigma(2) > 0, such that var(root n(R...
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作者：Mourrat, Jean-Christophe; Nolen, James
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); Duke University
摘要：In the homogenization of divergence-form equations with random coefficients, a central role is played by the corrector. We focus on a discrete space setting and on dimension 3 and more. Under a minor smoothness assumption on the law of the random coefficients, we identify the scaling limit of the corrector, which is akin to a Gaussian free field. This completes the argument started in [Ann. Probab. 44 (2016) 3207-3233].
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作者：Pillai, Natesh S.; Smith, Aaron
作者单位：Harvard University; University of Ottawa
摘要：Determining the mixing time of Kac's random walk on the sphere Sn-1 is a long-standing open problem. We show that the total variation mixing time of Kac's walk on Sn-1 is between 1/2n log(n) and 200n log(n) for all n sufficiently large. Our bound is thus optimal up to a constant factor, improving on the best-known upper bound of O(n(5) log(n)(2)) due to Jiang [Ann. AppL Probab. 22 (2012) 1712-1727]. Our main tool is a non-Markovian coupling recently introduced by the second author in [Ann. App...
