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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       font style='font-size:12px;'> 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       font style='font-size:12px;'> 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...
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 ...
FLUCTUATIONS OF THE BOSE-EINSTEIN CONDENSATE     Bose Einstein  condensed matter  volatility       font style='font-size:12px;'> 2015/7/7
FLUCTUATIONS OF THE BOSE-EINSTEIN CONDENSATE。
In probability theory, equalities are much less than inequalities. In this paper, we find a series of equalities which characterize the symmetry of the forming times of a family of similar cycles fo...
Abstract: A corrector theory for the strong approximation of fields inside composites made from two materials with different power law behavior is provided. The correctors are used to develop bounds o...
We consider transient random walks in random environment on Z in the positive speed (ballistic) and critical zero speed regimes. A classical result of Kesten, Kozlov and Spitzer proves that the hitti...
We study the distribution and various properties of exponential functionals of hypergeometric L´evy processes. We derive an explicit formula for the Mellin transform of the exponential function...
We study an infinite system of independent symmetric random walks on a hierarchical group, in particular, the c-random walks. Such walks are used, e.g., in population genetics. The number variance pr...
Sub-logarithmic fluctuations for internal DLA     Sub-logarithmic fluctuations  internal DLA       font style='font-size:12px;'> 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...
Phenological timing -- i.e. the course of annually recurring development stages in nature -- is of particular interest since it can be understood as a proxy for the climate at a specific region; moreo...
Nonequilibrium fluctuations of a tagged, or distinguished particle in a class of one dimensional mean-zero zero-range systems with sublinear, increasing rates are derived. In Jara-Landim-Sethuraman (2...
Within the abstract framework of dynamical system theory we describe a general approach to the Transient (or Evans-Searles) and Steady State (or Gallavotti-Cohen) Fluctuation Theorems of non-equilibr...
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...

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