5 citations · 5 across the 2 of their papers we have counts for
7 papers
On hydrodynamic limits in Sinai-type random environments
Claudio Landim, Carlos G. Pacheco, Sunder Sethuraman +1
We investigate the hydrodynamical behavior of a system of random walks with zero-range interactions moving in a common `Sinai-type' random environment on a one dimensional torus. T…
A density for the local time of the Brox diffusion
Jonathan Gutierrez-Pavón, Carlos G. Pacheco
We give explictly the probability density of the local time of the Brox diffusion at first passage times. Such formula is used to find the moments and to related the minima and max…
Inverting weak random operators
Jonathan Gutierrez-Pavón, Carlos G. Pacheco
We analyze two weak random operators, initially motivated from processes in random environment. Intuitively speaking these operators are ill-defined, but using bilinear forms one c…
The killed Brox diffusion
Jonathan Gutierrez-Pavón, Carlos G. Pacheco
We carry out an study of the Brox diffusion with killing. It turns out that when leaving fixed the environment one is able to recast some theory of diffusion and differential opera…
Random eigenvalues from a stochastic heat equation
Carlos Gabriel Pacheco
In this paper we prove the convergence of the eigenvalues of a random matrix that approximates a random Schrödinger operator. Originally, such random operator arises from a stochas…
From the Sinai's walk to the Brox diffusion using bilinear forms
Carlos Gabriel Pacheco
Using the generators, we establish a connection between the Sinai's random walk and the so-called Brox process. We first find the Dirichlet form of the Brox diffusion, and then pro…