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作者：Bufetov, Alexey; Ferrari, Patrik L.
作者单位：University of Bonn
摘要：We consider the totally asymmetric simple exclusion process (TASEP) with two different initial conditions with shock discontinuities formed by blocks of fully packed particles. Initially a second class particle is at the left of a shock discontinuity. Using multicolored TASEP we derive exact formulas for the distribution of the second class particle and colored height functions. These are given in terms of the height function at different positions of a single TASEP configuration. We study the...
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作者：Blanca, Antonio; Caputo, Pietro; Parisi, Daniel; Sinclair, Alistair; Vigoda, Eric
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Roma Tre University; University of California System; University of California Berkeley; University System of Georgia; Georgia Institute of Technology
摘要：We study the mixing time of the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models on the integer lattice Z(d). This dynamics is a widely used Markov chain that has largely resisted sharp analysis because it is nonlocal, that is, it changes the entire configuration in one step. We prove that, whenever strong spatial mixing (SSM) holds, the mixing time on any n-vertex cube in Z(d) is O (log n), and we prove this is tight by establishing a matching lower bound on the mixing time...
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作者：Kramkov, Dmitry; Xu, Yan
作者单位：Carnegie Mellon University
摘要：We study a single-period optimal transport problem on R-2 with a covariance-type cost function c(x,y)=(x(1)-y(1))(x(2)-y(2)) and a backward martingale constraint. We show that a transport plan gamma is optimal if and only if there is a maximal monotone set G that supports the x-marginal of gamma and such that c(x, y) = min(z is an element of G) c(z,y) for every (x,y) is an element of supp gamma. We obtain sharp regularity conditions for the uniqueness of an optimal plan and for its representat...
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作者：Lacoin, Hubert
摘要：In the present paper, we show that (under some minor technical assumption) Complex Gaussian multiplicative chaos defined as the complex exponential of a log-correlated Gaussian field can be obtained by taking the limit of the exponential of the field convoluted with a smoothing kernel. We consider two types of chaos: e(gamma)(X) for a log correlated field X and gamma = alpha + i beta, alpha, beta is an element of R and e(alpha X+)(i beta)(Y) for X and Y two independent fields with alpha, beta ...
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作者：Morina, Giulio; Latuszynski, Krzysztof; Nayar, Piotr; Wendland, Alex
作者单位：University of Warwick; University of Warsaw; University of Warwick
摘要：Given a p-coin that lands heads with unknown probability p, we wish to produce an f (p)-coin for a given function f : (0, 1) -> (0, 1). This problem is commonly known as the Bernoulli factory and results on its solvability and complexity have been obtained in (ACM Trans. Model. Comput. Simul. 4 (1994) 213-219; Ann. Appl. Probab. 15 (2005) 93-115). Nevertheless, generic ways to design a practical Bernoulli factory for a given function f exist only in a few special cases. We present a constructi...
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作者：Graham, Carl
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS)
摘要：Regenerative properties of the linear Hawkes process are proved under minimal assumptions on the transfer function, which may have unbounded support. For this, an original construction of the Hawkes process as a functional of a Poisson point process is derived from the immigration-birth representation, and the independence properties of the Poisson point process are exploited to exhibit regeneration times which are anticipative and not even measurable w.r.t. the Hawkes process. The regeneratio...
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作者：Peigne, Marc; Woess, Wolfgang
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Orleans; Universite de Tours; Graz University of Technology
摘要：Let X = (X-1, X-2) be a two-dimensional random variable and X(n), n is an element of N, a sequence of i.i.d. copies of X. The associated random walk is S(n) = X(1)+ ... + X(n). The corresponding absorbed-reflected walk W(n), n is an element of N, in the first quadrant is given by W(0) = x is an element of R-+(2) and W(n) = max{0, W(n - 1) - X(n)}, where the maximum is taken coordinate-wise. This is often called the Lindley process and models the waiting times in a two-server queue. We characte...
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作者：Budhiraja, Amarjit; Friedlander, Eric; Wu, Ruoyu
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of Chicago; Iowa State University
摘要：The join-the-shortest-queue routing policy is studied in an asymptotic regime where the number of processors n scales with the arrival rate. A large deviation principle (LDP) for the occupancy process is established, as n -> infinity, in a suitable infinite-dimensional path space. Model features that present technical challenges include, Markovian dynamics with discontinuous statistics, a diminishing rate property of the transition probability rates, and an infinite-dimensional state space. Th...
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作者：Heiny, Johannes; Mikosch, Thomas; Yslas, Jorge
作者单位：Ruhr University Bochum; University of Copenhagen
摘要：We study point process convergence for sequences of i.i.d. random walks. The objective is to derive asymptotic theory for the extremes of these random walks. We show convergence of the maximum random walk to the Gumbel distribution under the existence of a (2 + delta)th moment. We make heavy use of precise large deviation results for sums of i.i.d. random variables. As a consequence, we derive the joint convergence of the off-diagonal entries in sample covariance and correlation matrices of a ...
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作者：Jaber, Eduardo Abi; Cuchiero, Christa; Larsson, Martin; Pulido, Sergio
作者单位：University of Vienna; Carnegie Mellon University; Ecole Nationale Superieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：We obtain general weak existence and stability results for stochastic convolution equations with jumps under mild regularity assumptions, allowing for non-Lipschitz coefficients and singular kernels. Our approach relies on weak convergence in L-p spaces. The main tools are new a priori estimates on Sobolev-Slobodeckij norms of the solution, as well as a novel martingale problem that is equivalent to the original equation. This leads to generic approximation and stability theorems in the spirit...
