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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
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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...
Logarithmic Fluctuations for Internal DLA
Logarithmic Fluctuations Internal DLA
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2015/8/14
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
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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
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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 ...
Sub-logarithmic fluctuations for internal DLA
Sub-logarithmic fluctuations internal DLA
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2010/11/23
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
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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...