We use a combinatorial approach to study the trajectory of a light ray constrained to Euclidian plane R^2 with random reflecting obstacles placed throughout R^2. For the 2D Lorentz lattice gas (LLG) model we derive an analogue of Russo's formula of increasing events in percolation.
In this paper we extend the results of the research started by the first author in which Karlin-McGregor diagonalization of certain reversible Markov chains over countably infinite general state spaces by orthogonal polynomials was used to estimate the rate of convergence to a stationary distribution. We use a method of...
We solve a class of identification problems for nonparametric and semiparametric models when the endogenous covariate is discrete with unbounded support. Then we proceed with an approach that resolves a polynomial basis problem for the above class of discrete distributions, and for the distributions given in the sufficient condition for...
We construct a quantum interchange walk, related to classical walks with memory. This gives us a coinless discrete walk, while the origin in classical walks with memory offers the promise of use of existing tools from classical memoried walks. This approach readily reproduces all standard approaches. We briefly discuss its...
For the probabilistic model of shuffling by random transpositions we provide a coupling construction
with the expected coupling time of order C*n*log(n), where C is a moderate constant. We enlarge the
methodology of coupling by including intuitive non-Markovian coupling rules. We discuss why a typical
Markovian coupling is not always...
In recent years quantum random walks have garnered much interest among quantum information researchers. Part of the reason is the prospect that many hard problems can be solved efficiently by employing algorithms based on quantum random walks, in the same way that classical random walks have played a central role...