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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：Kabluchko, Zakhar; Marynych, Alexander
作者单位：University of Munster; Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv
摘要：Let xi 1, xi 2, ... be a sequence of independent copies of a random vector in R-d having an absolutely continuous distribution. Consider a random walk S-i := xi(1) + ... + ... + xi(i), and let C-n,C-d := conv(0, S-1, S-2, ..., S-n) be the convex hull of the first n+ 1 points it has visited. The polytope C-n,C-d is called k-neighborly if for any indices 0 <= i(1) < ... < i(k) <= n the convex hull of the k points S-i1 , ..., S-ik is a (k - 1)-dimensional face of C-n,C-d. We study the probability...
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作者：Barraquand, Guillaume; Corwin, Ivan
作者单位：Columbia University; Universite PSL; Ecole Normale Superieure (ENS); Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite
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作者：Lee, Jungkyoung; Seo, Insuk
作者单位：Seoul National University (SNU); Seoul National University (SNU)
摘要：In this article, we prove the Eyring-Kramers formula for non-reversible metastable diffusion processes that have a Gibbs invariant measure. Our result indicates that non-reversible processes exhibit faster metastable transitions between neighborhoods of local minima, compared to the reversible process considered in Bovier et al. (J Eur Math Soc 6:399-424, 2004). Therefore, by adding non-reversibility to the model, we can indeed accelerate the metastable transition. Our proof is based on the po...
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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...
