5 citations · 12 across the 6 of their papers we have counts for
9 papers
Toeplitz operators in Bergman space induced by radial measures
Egor A. Maximenko, Carlos G. Pacheco
We study radial Carleson--Bergman measures on the unit disk and the corresponding Toeplitz operators acting in the Bergman space. First, we show that such Toeplitz operators are di…
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…
Green kernel for a random Schrödinger operator
Carlos G. Pacheco
We find explicitly the Green kernel of a random Schrödinger operator with Brownian white noise. To do this, we first handle the random operator by defining it weakly using the inne…
Picard iterations for diffusions on symmetric matrices
Carlos G. Pacheco
Matrix-valued stochastic processes have been of significant importance in areas such as physics, engineering and mathematical finance. One of the first models studied has been the…