Spectral analysis of random walk operators on euclidean space

Some Problems on Random Walk in Space

Consider the lattice formed by all points whose coordinates are integers in d-dimensional Euclidean space, and let a point S j(n) perform a move randomly on this lattice according to the following rules : At time zero it is at the origin and if at any time n-1 (n = 1, 2. .. .) it is at some point S then at time t it will be at one of the 2d lattice points nearest S, the probability of it being ...

Anomalies of Dirac Type Operators on Euclidean Space

Spectral Sparsification of Random-Walk Matrix Polynomials

We consider a fundamental algorithmic question in spectral graph theory: Compute a spectral sparsifier of a random-walk matrix-polynomial

Non-euclidean structure of spectral color space

Color processing methods can be divided into methods based on human color vision and spectral based methods. Human vision based methods usually describe color with three parameters which are easy to interpret since they model familiar color perception processes. They share however the limitations of human color vision such as metamerism. Spectral based methods describe colors by their underlyin...

Random Walk Models for Space-fractional Diiusion Processes Random Walk Models for Space-fractional Diiusion Processes

By space-fractional (or L evy-Feller) diiusion processes we mean the processes governed by a generalized diiusion equation which generates all L evy stable probability distributions with index (0 < 2), including the two symmetric most popular laws, Cauchy (= 1) and Gauss (= 2). This generalized equation is obtained from the standard linear diiusion equation by replacing the second-order space d...