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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...
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作者：Feray, Valentin; Louf, Baptiste; Thevenin, Paul
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine
摘要：We study the asymptotic behaviour of random factorizations of the n-cycle into transpositions of fixed genus g > 0. They have a geometric interpretation as branched covers of the sphere and their enumeration as Hurwitz numbers was extensively studied in algebraic combinatorics and enumerative geometry. On the probabilistic side, several models and properties of permutation factorizations were studied in previous works, in particular minimal factorizations of cycles into transpositions (which c...
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作者：Ganguly, Shirshendu; Nam, Kyeongsik
作者单位：University of California System; University of California Berkeley; Korea Advanced Institute of Science & Technology (KAIST)
摘要：Large deviation behavior of the largest eigenvalue lambda(1) of Wigner matrices including those arising from an Erdos-Renyi random graph G(n, p) with i.i.d. random conductances on the edges has been the topic of considerable interest. However, despite several recent advances, not much is known when the underlying graph is sparse i.e., p -> 0, except the recent works (Bhattacharya et al., Ann Probab 49(4):1847-1885, 202 land Bhattacharya and Ganguly, SIAM J Discret Math, 2020) which consider th...
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作者：Bloznelis, Mindaugas; Goetze, Friedrich
作者单位：Vilnius University; University of Bielefeld
摘要：We study the distribution of a general class of asymptotically linear statistics which are symmetric functions of N independent observations. The distribution functions of these statistics are approximated by an Edgeworth expansion with a remainder of order o(N-1). The Edgeworth expansion is based on Hoeffding's decomposition which provides a stochastic expansion into a linear part, a quadratic part as well as smaller higher order parts. The validity of this Edgeworth expansion is proved under...
