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Metastability for Non-Linear Random Perturbations of Dynamical Systems
Quasi linear parabolic equation the small parameter the second order items
2015/9/28
In this paper we describe the long time behavior of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of the corresponding di@...
A sharp bound on the L2 norm of the solution of a random elliptic difference equation
sharp bound L2 norm random elliptic difference equation
2015/7/14
We consider a stationary solution of the Poisson equation (λ − Lω)φλ(x; ω) = −∂∗b(x; ω), where λ > 0 and Lω is a random, discrete, elliptic operator given by Lωu(x) := ∂&...
Entropy power inequality for a family of discrete random variables
Entropy power inequality family of discrete random variables
2011/1/17
It is known that the Entropy Power Inequality (EPI) always holds if the random variables have density. Not much work has been done to identify discrete distributions for which the inequality holds wit...
Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus
Growth of Weil-Petersson volumes random hyperbolic surfaces of large genus
2011/1/20
In this paper, we investigate the geometric properties of hyperbolic surfaces by studying the lengths of simple closed geodesics. The moduli space Mg,n of complete hyperbolic surfaces of genus g ≥ 2 w...
Lack of Spectral Gap and Hyperbolicity in Asymptotic Erdös-Renyi Random Graphs
Spectral Gap Hyperbolicity Asymptotic Erdö s-Renyi Random Graphs
2010/12/14
In this work, we prove the absence of a spectral gap for the normalized Laplacian of the Erdos-Renyi random graph G(n; p) when p = d n for d > 1 as n ! 1. We also prove that for any positive the Er...
On the effect of random inhomogeneities in Kerr-media modelled by non-linear Schrodinger equation
Kerr-media modelled non-linear Schrodinger equation
2010/4/6
We consider propagation of optical pulses under the interplay of dispersion and Kerr non-linearity in optical fibres with impurities distributed at random uniformly on the fibre. By using a model base...
We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity k between the elements of the network. We show that this class of networks exhibit an order-cha...