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2018随机矩阵与自由概率论研讨会(Workshop on Random Matrices and Free Probability Theory)
2018 随机矩阵与自由概率论 研讨会
2017/12/20
The workshop will explore large-N asymptotics of random matrices, in connection with the operator-algebra models of their limiting behavior that appear in free probability theory. The behavior or rand...
Extreme values for two-dimensional discrete Gaussian free field
Extreme values two-dimensional discrete Gaussian free field Probability
2012/6/15
We consider in this paper the collection of near maxima of the discrete, two dimensional Gaussian free field in a box with Dirichlet boundary conditions. We provide a rough description of the geometry...
Multidimensional semicircular limits on the free Wigner chaos
Convergence in Distribution Fourth Moment Condition Free BrownianMotion Free Probability Multidimensional Limit Theorems
2011/9/21
Abstract: We show that, for sequences of vectors of multiple Wigner integrals with respect to a free Brownian motion, componentwise convergence to semicircular is equivalent to joint convergence. This...
Free Completely Random Measures
Bayesian non parametrics Bercovici-Pata bijection free completely random measures free infinite divisibility free probability
2011/9/15
Abstract: Free probability is a noncommutative probability theory introduced by Voiculescu where the concept of independence of classical probability is replaced by the concept of freeness. An importa...
SIR epidemics on a scale-free spatial nested modular network with a non-trivial threshold
Epidemics SIR Reed-Frost percolation long-range directed scale-free modular nested communities hierarchical
2011/8/30
Abstract: We propose a class of random scale-free spatial networks with nested community structures and analyze Reed-Frost epidemics with community related independent transmissions. We show that the ...
An inequality for the distance between densities of free convolutions
densities of free convolutions inequality Probability
2011/8/24
Abstract: It is shown that under some conditions the distance between densities of free convolutions of two pairs of probability measures is smaller than the maximum of the Levy distance between the c...
Abstract: We discuss the distributions of three functionals of the free Brownian bridge: its $\L^2$-norm, the second component of its signature and its L\'evy area. All of these are freely infinitely ...
Filtering of continuous-time Markov chains with noise-free observation and applications
Filtering of continuous-time Markov chains noise-free observation applications
2010/11/30
Let X be a continuous-time Markov chain in a finite set I, let h be a mapping of I onto another set, and let Y be defined by Yt = h(Xt), (t ≥ 0). We address the filtering problem
for X in terms of th...
A Khintchine Decomposition for Free Probability
Khintchine Decomposition Free Probability
2010/12/13
Let μ be a probability measure on the real line. In this paper we prove that there exists a decomposition μ = μ0 ⊞μ1 ⊞· · ·⊞μn ⊞· · · such that μ0 is infinitely divisible and μ...