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One-dimensional model of interacting-step fluctuations on vicinal surfaces:Analytical formulas and kinetic Monte Carlo simulations
One-dimensional model interacting-step fluctuations vicinal surfaces Analytical formulas kinetic Monte Carlo simulations
2015/10/16
We study analytically and numerically a one-dimensional model of interacting line defects steps fluctuating on a vicinal crystal. Our goal is to formulate and validate analytical techniques for appr...
Let each of n particles starting at the origin in Z2 perform simple random walk until reaching a site with no other particles. Lawler, Bramson, and Griffeath proved that the resulting random set A(n) ...
Limit of fluctuations of solutions of Wigner Equation
fluctuations of solutions Wigner Equation
2015/7/14
We consider fluctuations of the solution W ε(t, x, k) of the Wigner equation, which describes energy evolution of a solution of the Schr¨odinger equation with a random white noise in time potential. T...
Fluctuations of solutions to Wigner equation with an Ornstein-Uhlenbeck potential
Fluctuations of solutions Wigner equation Ornstein-Uhlenbeck potential
2015/7/14
We consider energy fluctuations for solutions of the Schrodinger equation with an OrnsteinUhlenbeck random potential when the initial data is spatially localized. The limit of the fluctuations of the ...
We consider internal diffusion limited aggregation in dimension larger or equal to two. This is a random cluster growth model, where random walks start at the origin of the $d$-dimensional lattice, o...
Current fluctuations for independent random walks in multiple dimensions
Independent random walks hydrodynamic limit current Independent random walks
2010/12/6
Consider a system of particles evolving as independent and iden-tically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity ~v, the c...