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作者：Breuillard, Emmanuel; Varju, Peter P.
作者单位：University of Oxford; University of Cambridge
摘要：We study the Markov chain x(n+1 )= ax(n) + b(n) on a finite field F-p, where a is an element of F-p(x) is fixed and b(n) are independent and identically distributed random variables in F-p. Conditionally on the Riemann hypothesis for all Dedekind zeta functions, we show that the chain exhibits a cut-off phenomenon for most primes p and most values of a is an element of F-p(x). We also obtain weaker, but unconditional, upper bounds for the mixing time.
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作者：Osada, Hirofumi; Shirai, Tomoyuki
作者单位：Kyushu University; Kyushu University
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作者：Korotkikh, Sergei
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We study a new integrable probabilistic system, defined in terms of a stochastic colored vertex model on a square lattice. The main distinctive feature of our model is a new family of parameters attached to diagonals rather than to rows or columns, like in other similar models. Because of these new parameters the previously known results about vertex models cannot be directly applied, but nevertheless the integrability remains, and we prove explicit integral expressions for q-deformed moments ...
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作者：Doebler, Christian; Kasprzak, Mikolaj; Peccati, Giovanni
作者单位：Heinrich Heine University Dusseldorf; University of Luxembourg; Massachusetts Institute of Technology (MIT)
摘要：We prove a multivariate functional version of de Jong's CLT (J Multivar Anal 34(2):275-289, 1990) yielding that, given a sequence of vectors of Hoeffdingdegenerate U-statistics, the corresponding empirical processes on [0, 1] weakly converge in the Skorohod space as soon as their fourth cumulants in t = 1 vanish asymptotically and a certain strengthening of the Lindeberg-type condition is verified. As an application, we lift to the functional level the 'universality of Wiener chaos' phenomenon...
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作者：Chen, Xinxing; Hu, Yueyun; Shi, Zhan
作者单位：Shanghai Jiao Tong University
摘要：We are interested in the recursive model (Y-n, n >= 0) studied by Collet et al. (Commun Math Phys 94:353-370, 1984) and by Derrida and Retaux (J Stat Phys 156:268-290, 2014). We prove that at criticality, the probability P(Y-n > 0) behaves like n(-2+o(1)) as n goes to infinity; this gives a weaker confirmation of predictions made in Collet et al. (1984), Derrida and Retaux (2014) and Chen et al. (in: Sidoravicius (ed) Sojourns in probability theory and statistical physics-III, Springer, Singap...
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作者：Gao, Pu; Isaev, Mikhail; McKay, Brendan D.
作者单位：University of Waterloo; Monash University; Australian National University
摘要：Kim and Vu made the following conjecture (Advances in Mathematics, 2004): if d >> log n, then the random d-regular graph G(n, d) can asymptotically almost surely be sandwiched between G(n, p(1)) and G(n, p(2)) where p(1) and p(2) are both (1 + o(1))d/n. They proved this conjecture for log n << d >= n(1/3-o(1)), with a defect in the sandwiching: G(n, d) contains G(n, p(1)) perfectly, but is not completely contained in G(n, p(2)). The embedding G(n, p(1)) subset of G(n, d) was improved by Dudek,...
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作者：De Raynal, Paul-Eric Chaudru; Honore, Igor; Menozzi, Stephane
作者单位：Nantes Universite; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universite Paris Saclay; HSE University (National Research University Higher School of Economics)
摘要：We establish strong uniqueness for a class of degenerate SDEs of weak Hormander type under suitable Holder regularity conditions for the associated drift term. Our approach relies on the Zvonkin transform which requires to exhibit good smoothing properties of the underlying parabolic PDE with rough, here Holder, drift coefficients and source term. Such regularizing effects are established through a perturbation technique (forward parametrix approach) which also heavily relies on appropriate du...
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作者：Ahn, Andrew
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We study Markov chains formed by squared singular values of products of truncated orthogonal, unitary, symplectic matrices (corresponding to the Dyson index beta = 1, 2, 4 respectively) where time corresponds to the number of terms in the product. More generally, we consider the beta-Jacobi product process obtained by extrapolating to arbitrary beta > 0. For fixed time (i.e. number of factors is constant), we show that the global fluctuations are jointly Gaussian with explicit covariances. For...
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作者：Aidekon, Elie; Da Silva, William
作者单位：Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France; Sorbonne Universite; Universite Paris Cite
摘要：The aim of this paper is to present a self-similar growth-fragmentation process linked to a Brownian excursion in the upper half-plane H, obtained by cutting the excursion at horizontal levels. We prove that the associated growth-fragmentation is related to one of the growth-fragmentation processes introduced by Bertoin, Budd, Curien and Kortchemski in (Bertoin et al. Probab Theory Relat Field 172:663-724, 2018).
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作者：Holroyd, Alexander E.; Janson, Svante; Wastlund, Johan
作者单位：University of Bristol; Uppsala University; Chalmers University of Technology
摘要：Suppose that red and blue points form independent homogeneous Poisson processes of equal intensity in R-d. For a positive (respectively, negative) parameter gamma we consider red-blue matchings that locally minimize (respectively, maximize) the sum of gamma th powers of the edge lengths, subject to locally minimizing the number of unmatched points. The parameter can be viewed as a measure of fairness. The limit gamma -> -infinity is equivalent to Gale-Shapley stable matching. We also consider ...
