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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent developments on random hyperbolic surfaces of large genus
大属随机 双曲曲面 球面几何
2023/4/21
In this talk, we report several very recent asymptotic results on certain classical geometric quantities viewed as random variables on the moduli space of Riemann surfaces for large genus (and many cu...
EXCURSIONS AND OCCUPATION TIMES OF CRITICAL EXCITED RANDOM WALKS
EXCURSIONS AND OCCUPATION TIMES EXCITED RANDOM WALKS
2015/9/29
We consider excited random walks (ERWs) on integers in i.i.d. environments with a bounded number of excitations per site. The emphasis is primarily on
the critical case for the transition between rec...
THE VISITS TO ZERO OF A RANDOM WALK DRIVEN BY AN IRRATIONAL ROTATION
RANDOM WALK DRIVEN IRRATIONAL ROTATION
2015/9/29
The method is to nd the asymptotic behavior of the ergodic sums of L1
functions for linear
ows on the in nite staircase surface.
Our methods also provide a new proof of J. Beck's central limit th...
Random walks on finite rank solvable groups
random walk heat kernel decay asymptotic invariants of infinite groups Prüfer rank – solvable group
2015/8/26
We establish the lower bound p2t (e, e) exp(−t1/3), for the large times asymptotic
behaviours of the probabilities p2t (e, e) of return to the origin at even times 2t, for
random walks assoc...
Mixing times for random walks on geometric random graphs
Random geometric random graph nodes wireless network model and threshold properties random walk figure d dimension
2015/8/11
A geometric random graph, G^d(n,r), is formed as follows: place n nodes uniformly at random onto the surface of the d-dimensional unit torus and connect nodes which are within a distance r of each oth...
Tight Oracle Bounds for Low-rank Matrix Recovery from a Minimal Number of Random Measurements
Matrix completion The Dantzig selector oracle inequalities norm of random matrices convex optimization and semidefinite programming
2015/6/17
This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that pro...
On rainbow-k-connectivity of random graphs
Rainbow connectivity Random graph Graph algorithms Sharp threshold function Probabilistic method
2012/12/4
A path in an edge-colored graph is called a rainbow path if the edges on it have distinct colors. For k 1, the rainbow-k-connectivity of a graph G, denoted by rck(G), is the minimum number of colors...
On the distribution of angles between the N shortest vectors in a random lattice
distribution of angles N shortest vectors random lattice
2011/2/21
We determine the joint distribution of the lengths of, and angles between, the N shortest lattice vectors in a random n-dimensional lattice as n ! 1. Moreover we interpret the result in terms of eigen...
Kernel random matrices have attracted a lot of interest in recent years, from both practical and theoretical standpoints. Most of the theoretical work so far has focused on the case were the data is s...
CLT for spectra of submatrices of Wigner random matrices II. Stochastic evolution
CLT submatrices Wigner random matrices II Stochastic evolution
2010/11/22
We show that the global fluctuations of spectra of GOE and GUE matrices and their principal submatrices executing Dyson's Brownian motion are Gaussian in the limit of large matrix dimensions. For nest...
Introduction to the non-asymptotic analysis of random matrices
the non-asymptotic analysis of random matrices math
2010/11/19
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices wi...
Given a large, high-dimensional sample from a spiked population, the top sample covariance eigenvalue is known to exhibit a phase transition. We show that the largest eigenvalues have asymptotic dist...
Let be a random spherical triangle (meaning that vertices are independent and uniform on the unit sphere). A closed-form expression for the area density of has been known since 1867; a complicated...
Addendum to "Energies of zeros of random sections on Riemann surfaces" [arXiv:0705.2000]. Indiana Univ. Math. J. 57 (2008), no. 4, 1753-1780
Energies of zeros of random sections Riemann surfaces
2010/12/9
The purpose of this note is to resolve an apparent discrepancy between the calculations
in the article [ABS] of Armentano- Beltran-Shub (henceforth ABS) and that in Qi Zhong’s
article [Zh] of the as...
On Some fundamental aspects of Polyominoes on Random Voronoi Tilings
fundamental aspects Polyominoes Random Voronoi Tilings
2010/12/9
Consider a Voronoi tiling of Rd based on a realization of a inhomogeneous Poisson random set. A Voronoi polyomino is a finite and connected union of Voronoi tiles.In this paper we provide tail bounds ...