-
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...
-
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...
-
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,...
-
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...
-
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
-
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...
-
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...
-
作者：Athreya, Jayadev S.; Mj, Mahan; Roy, Parthanil
作者单位：University of Washington; University of Washington Seattle; Tata Institute of Fundamental Research (TIFR); Indian Statistical Institute; Indian Statistical Institute Bangalore
摘要：We study extreme values of group-indexed stable random fields for discrete groups G acting geometrically on spaces X in the following cases: (1) G acts properly discontinuously by isometries on a CAT(-1) space X, (2) G is a lattice in a higher rank Lie group, acting on a symmetric space X, and (3) G is the mapping class group of a surface acting on its Teichmuller space. The connection between extreme values and the geometric action is mediated by the action of the group G on its limit set equ...
-
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...
-
作者：Bobrowski, Omer
作者单位：Technion Israel Institute of Technology; University of London; Queen Mary University London
摘要：We study the homology of random Cech complexes generated by a homogeneous Poisson process. We focus on 'homological connectivity'-the stage where the random complex is dense enough, so that its homology stabilizes and becomes isomorphic to that of the underlying topological space. Our results form a comprehensive high-dimensional analogue of well-known phenomena related to connectivity in the Erdos-Renyi graph and random geometric graphs. We first prove that there is a sequence of sharp phase ...
