-
作者：Lelarge, Marc; Miolane, Leo
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Inria
摘要：We consider the high-dimensional inference problem where the signal is a low-rank symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension setting for the mutual information between the signal and the observations, as well as the matrix minimum mean squared error, while the rank of the signal remains constant. We also show that our model extends beyond the particular case of additive Gaus...
-
作者：Ajanki, Oskari H.; Erdos, Laszlo; Krueger, Torben
作者单位：Institute of Science & Technology - Austria
摘要：We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent.
-
作者：Mytnik, Leonid; Perkins, Edwin
作者单位：Technion Israel Institute of Technology; University of British Columbia
摘要：We show that the Hausdorff dimension of the boundary of d-dimensional super-Brownian motion is 0, if d=1, 4-22, if d=2, and (9-17)/2, if d=3.
-
作者：Rodriguez, Pierre-Francois
作者单位：University of California System; University of California Los Angeles
摘要：We define two families of Poissonian soups of bidirectional trajectories onZ2, which can be seen to adequately describe the local picture of the trace left by a random walk on the two-dimensional torus (Z/NZ)2, started from the uniform distribution, run up to a time of order (NlogN)2 and forced to avoid a fixed point. The local limit of the latter was recently established inComets et al. (Commun Math Phys 343:129-164, 2016). Our construction proceeds by considering, somewhat in the spirit of s...
-
作者：Fang, Xiao; Shao, Qi-Man; Xu, Lihu
作者单位：Chinese University of Hong Kong; University of Macau
-
作者：Liu, Xuan; Qian, Zhongmin
作者单位：University of Oxford
摘要：By using analytic tools from stochastic analysis, we initiate a study of some non-linear parabolic equations on Sierpinski gasket, motivated by modellings of fluid flows along fractals (which can be considered as models of simplified rough porous media). Unlike the regular space case, such parabolic type equations involving non-linear convection terms must take a different form, due to the fact that convection terms must be singular to the linear part which defines the heat semigroup. In order...
-
作者：Freslon, Amaury
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：We give bounds in total variation distance for random walks associated to pure central states on free orthogonal quantum groups. As a consequence, we prove that the analogue of the uniform plane Kac walk on this quantum group has a cut-off at Nln(N)/2(1-cos(theta)). This is the first result of this type for genuine compact quantum groups. We also obtain similar results for mixtures of rotations and quantum permutations.
-
作者：Levine, Lionel; Silvestri, Vittoria
作者单位：Cornell University; University of Cambridge
摘要：Internal DLA is a discrete model of a moving interface. On the cylinder graph ZNxZ, a particle starts uniformly on ZNx{0} and performs simple random walk on the cylinder until reaching an unoccupied site in ZNxZ >= 0, which it occupies forever. This operation defines a Markov chain on subsets of the cylinder. We first show that a typical subset is rectangular with at most logarithmic fluctuations. We use this to prove that two Internal DLA chains started from different typical subsets can be c...
-
作者：Conforti, Giovanni
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：The Schrodinger problem is obtained by replacing the mean square distance with the relative entropy in the Monge-Kantorovich problem. It was first addressed by Schrodinger as the problem of describing the most likely evolution of a large number of Brownian particles conditioned to reach an unexpected configuration. Its optimal value, the entropic transportation cost, and its optimal solution, the Schrodinger bridge, stand as the natural probabilistic counterparts to the transportation cost and...
-
作者：Dahlqvist, Antoine; Diehl, Joscha; Driver, Bruce K.
作者单位：University College Dublin; Max Planck Society; University of California System; University of California San Diego
摘要：We show well-posedness for the parabolic Anderson model on 2-dimensional closed Riemannian manifolds. To this end we extend the notion of regularity structures to curved space, and explicitly construct the minimal structure required for this equation. A central ingredient is the appropriate re-interpretation of the polynomial model, which we build up to any order.
