Orthogonality and probability: mixing times (2009)
We produce the first example of bounding total variation distance to stationarity and estimating mixing times via orthogonal polynomials diagonalization of discrete reversible Markov chains, the...
A note on adiabatic theorem for Markov chains and adiabatic quantum computation (2009)
We derive an adiabatic theorem for Markov chains using well known facts about mixing and relaxation times. We discuss the results in the context of the recent developments in adiabatic quantum...
Occupation times via Bessel functions (2008)
Kovchegov, Yevgeniy, Meredith, Nick, Nir, Eyal
This study of occupation time densities for continuous-time Markov processes was inspired by the work of E.Nir et al (2006) in the field of Single Molecule FRET spectroscopy. There, a single molecule...
Orthogonality and probability: beyond nearest neighbor transitions (2008)
In this article, we will explore why Karlin-McGregor method of using orthogonal polynomials in the study of Markov processes was so successful for one dimensional nearest neighbor processes, but...
Mixing times via super-fast coupling (2006)
Burton, Robert, Kovchegov, Yevgeniy
We provide a coupling proof that the transposition shuffle on a deck of n cards is mixing of rate Cn(log{n}) with a moderate constant, C. This rate was determined by Diaconis and Shahshahani, but the...
Exclusion Processes with Multiple Interactions (2004)
We introduce the mathematical theory of the particle systems that interact via permutations, where the transition rates are assigned not to the jumps from a site to a site, but to the permutations...
Multi-particle processes with reinforcements (2004)
We consider a multi-particle generalization of linear edge-reinforced random walk (ERRW). We observe that in absence of exchangeability, new techniques are needed in order to study the multi-particle...
Linear Speed Large Deviations for Percolation Clusters (2003)
Kovchegov, Yevgeniy; UCLA Mathematics Department, USA; Yevgeniy@math.ucla.edu, Sheffield, Scott Roger; Microsoft Research; Sheff@microsoft.com
Let $C_n$ be the origin-containing cluster in subcritical percolation on the lattice $frac{1}{n} mathbb Z^d$, viewed as a random variable in the space $Omega$ of compact, connected, origin-containing...
Linear speed large deviations for percolation clusters (2003)
Kovchegov, Yevgeniy, Sheffield, Scott
Let C_n be the origin-containing cluster in subcritical percolation on the lattice (1/n) Z^d, viewed as a random variable in the space Omega of compact, connected, origin-containing subsets of R^d,...
Brownian Bridge and Self-Avoiding Random Walk (2002)
We establish the Brownian bridge asymptotics for a scaled self-avoiding walk conditioned on arriving to a far away point $n \vec{a}$ for $\vec{a}$ in $Z^d$, as $n$ increases to infinity.
Brownian bridge, percolation and related processes / (2002)
Kovchegov, Yevgeniy., Dembo, Amir Advisor
Submitted to the Department of Mathematics.
Brownian Bridge Asymptotics for the Subcritical Bernoulli Bond Percolation (2001)
For the d-dimensional model of a subcritical bond percolation (p