Deterministic approximations of random reflectors

Deterministic Approximations of Random Reflectors

Within classical optics, one may add microscopic “roughness” to a macroscopically flat mirror so that parallel rays of a given angle are reflected at different outgoing angles. Taking the limit (as the roughness becomes increasingly microscopic) one obtains a flat surface that reflects randomly, i.e., the transition from incoming to outgoing ray is described by a probability kernel (whose form ...

A Characterization of Random Approximations

By using Hahn-Banach theorem, a characterization of random approximations is obtained.

Deterministic Random Walks

Jim Propp’s P -machine, also known as ‘rotor router model’ is a simple deterministic process that simulates a random walk on a graph. Instead of distributing chips to randomly chosen neighbors, it serves the neighbors in a fixed order. We investigate how well this process simulates a random walk. For the graph being the infinite path, we show that, independent of the starting configuration, at ...

Random Deterministic Automata

In this article, we consider deterministic automata under the paradigm of average case analysis of algorithms. We present the main results obtained in the literature using this point of view, from the very beginning with Korshunov’s theorem about the asymptotic number of accessible automata to the most recent advances, such as the average running time of Moore’s state minimization algorithm or ...

Deterministic and Random Aspects Of