Add to ORKGWe study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus on explicit (hypergeometric) evaluations of the moment functions and probability densities in the case of up to five steps. Somewhat to our surprise, we are able to provide complete extensions to arbitrary dimensions for most of the central results known in the two-dimensional case.
We derive an explicit piecewise-polynomial closed form for the probability density function of the d...
Research Doctorate - Doctor of Philosophy (PhD)In the first quarter of this dissertation, we investi...
Consider a simple symmetric random walk on the line. The parts of the random walk between consecutiv...
We study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus o...
We study the densities of uniform random walks in the plane. A special focus is on the case of short...
with an appendix by: DON ZAGIER Abstract. We study the densities of uniform random walks in the plan...
We study the moments of the distance traveled by a walk in the plane with unit steps in random direc...
We study the moments of the distance traveled by a walk in the plane with unit steps in random direc...
Random walks of two steps, with fixed sums of lengths of $$1$$1, taken into uniformly random directi...
This paper considers the representation of odd moments of the distribution of a four-step uniform ra...
Abstract. We study the expected distance of a two-dimensional walk in the plane with unit steps in r...
We investigate the moments of 3-step and 4-step uniform random walk in the plane. In particular, we ...
In this paper, we cover some essential problems of (simple) random walks in one, two and three dimen...
We study the expected distance of a two-dimensional walk in the plane with unit steps in random dire...
We study the expected distance of a two-dimensional walk in the plane with unit steps in random dire...
We derive an explicit piecewise-polynomial closed form for the probability density function of the d...
Research Doctorate - Doctor of Philosophy (PhD)In the first quarter of this dissertation, we investi...
Consider a simple symmetric random walk on the line. The parts of the random walk between consecutiv...
We study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus o...
We study the densities of uniform random walks in the plane. A special focus is on the case of short...
with an appendix by: DON ZAGIER Abstract. We study the densities of uniform random walks in the plan...
We study the moments of the distance traveled by a walk in the plane with unit steps in random direc...
We study the moments of the distance traveled by a walk in the plane with unit steps in random direc...
Random walks of two steps, with fixed sums of lengths of $$1$$1, taken into uniformly random directi...
This paper considers the representation of odd moments of the distribution of a four-step uniform ra...
Abstract. We study the expected distance of a two-dimensional walk in the plane with unit steps in r...
We investigate the moments of 3-step and 4-step uniform random walk in the plane. In particular, we ...
In this paper, we cover some essential problems of (simple) random walks in one, two and three dimen...
We study the expected distance of a two-dimensional walk in the plane with unit steps in random dire...
We study the expected distance of a two-dimensional walk in the plane with unit steps in random dire...
We derive an explicit piecewise-polynomial closed form for the probability density function of the d...
Research Doctorate - Doctor of Philosophy (PhD)In the first quarter of this dissertation, we investi...
Consider a simple symmetric random walk on the line. The parts of the random walk between consecutiv...