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作者：Fukushima, Ryoki; Junk, Stefan
作者单位：University of Tsukuba; Tohoku University
摘要：We prove that the free energy of directed polymer in Bernoulli environment converges to the growth rate for the number of open paths in super-critical oriented percolation as the temperature tends to zero. Our proof is based on rate of convergence results which hold uniformly in the temperature. We also prove that the convergence rate is locally uniform in the percolation parameter inside the super-critical phase, which implies that the growth rate depends continuously on the percolation param...
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作者：Petrov, Leonid; Saenz, Axel
作者单位：Kharkevich Institute for Information Transmission Problems of the RAS; University of Virginia; University of Warwick
摘要：We obtain a new relation between the distributions mu(t) at different times t >= 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions mu(t) backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammers...
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作者：Kosygina, Elena; Mountford, Thomas; Peterson, Jonathon
作者单位：City University of New York (CUNY) System; Baruch College (CUNY); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Purdue University System; Purdue University
摘要：We consider one-dimensional excited random walks (ERWs) with i.i.d. Markovian cookie stacks in the non-boundary recurrent regime. We prove that under diffusive scaling such an ERW converges in the standard Skorokhod topology to a multiple of Brownian motion perturbed at its extrema (BMPE). All parameters of the limiting process are given explicitly in terms of those of the cookie Markov chain at a single site. While our results extend the results in Dolgopyat and Kosygina (Electron Commun Prob...
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作者：Aru, Juhan; Jego, Antoine; Junnila, Janne
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We consider the imaginary Gaussian multiplicative chaos, i.e. the complex Wick exponential mu(beta ):=: e(i beta Gamma(x)) : for a log-correlated Gaussian field Gamma in d >= 1 dimensions. We prove a basic density result, showing that for any nonzero continuous test function f, the complex-valued random variable mu(beta)(f) has a smooth density w.r.t. the Lebesgue measure on C. As a corollary, we deduce that the negative moments of imaginary chaos on the unit circle do not correspond to the an...
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作者：Erschler, Anna; Zheng, Tianyi
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); University of California System; University of California San Diego
摘要：We prove the law of large numbers for the drift of random walks on the two-dimensional lamplighter group, under the assumption that the random walk has finite (2 + epsilon)-moment. This result is in contrast with classical examples of abelian groups, where the displacement after n steps, normalised by its mean, does not concentrate, and the limiting distribution of the normalised n-step displacement admits a density whose support is [0, infinity). We study further examples of groups, some with...
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作者：Depersin, Jules; Lecue, Guillaume
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Ecole Polytechnique
摘要：We consider the problem of robust mean and location estimation with respect to any pseudo-norm of the form x is an element of R-d bar right arrow parallel to x parallel to(S) = sup(v is an element of S)< v, x > where S is any symmetric subset of R-d. We show that the deviation-optimal minimax sub-Gaussian rate for confidence 1 - delta is max (l*(Sigma S-1/2)/root N, sup(v is an element of S) parallel to Sigma(1/2)v parallel to(2) root log(1/delta)/N) where l*(Sigma S-1/2) is the Gaussian mean ...
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作者：Driver, Bruce K.; Hall, Brian; Kemp, Todd
作者单位：University of California System; University of California San Diego; University of Notre Dame
摘要：The free multiplicative Brownian motion b(t) is the large-N limit of the Brownian motion on GL(N; C), in the sense of (*)-distributions. The natural candidate for the large-N limit of the empirical distribution of eigenvalues is thus the Brown measure of b(t). In previous work, the second and third authors showed that this Brown measure is supported in the closure of a region Sigma(t) that appeared in the work of Biane. In the present paper, we compute the Brown measure completely. It has a co...
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作者：Yang, Kevin
作者单位：Stanford University
摘要：This paper has two main goals. The first is universality of the KPZ equation for fluctuations of dynamic interfaces associated to interacting particle systems in the presence of open boundary. We consider generalizations on the open-ASEP from Corwin and Shen (Commun Pure Appl Math 71(10):2065-2128, 2018), Parekh (Commun Math Phys 365:569-649, 2019. https://doi.org/10.1007/s00220-018-3258-x) . but admitting non-simple interactions both at the boundary and within the bulk of the particle system....
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作者：Chassagneux, Jean-Francois; Nadtochiy, Sergey; Richou, Adrien
作者单位：Universite Paris Cite; Universite Paris Cite; Illinois Institute of Technology; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：This paper establishes the well-posedness of reflected backward stochastic differential equations in non-convex domains that satisfy a weak version of the star-shaped property. The main results are established (i) in a Markovian framework with Holder-continuous generator and terminal condition and (ii) in a general setting under a smallness assumption on the input data. We also investigate the connections between this well-posedness result and the theory of martingales on manifolds, which, in ...
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作者：Ouaki, Mehdi
作者单位：University of California System; University of California Berkeley
摘要：The statistical description of the scalar conservation law of the form rho(t) = H(rho)(x) with H : R -> R a smooth convex function has been an object of interest when the initial profile rho(., 0) is random. The special case when H(rho) = rho(2)/2 (Burgers equation) has in particular received extensive interest in the past and is now understood for various random initial conditions. We prove in this paper a conjecture on the profile of the solution at any time t > 0 for a general class of Hami...
