The Problem of the Random Walk

  title={The Problem of the Random Walk},
  author={Karl Pearson},
CAN any of your readers refer me to a work wherein I should find a solution of the following problem, or failing the knowledge of any existing solution provide me with an original one? I should be extremely grateful for aid in the matter. 

Topics from this paper

Joint densities for random walks in the plane
We point out the existence of computationally convenient techniques for calculating the joint probability density for the position of a Pearson random walk after n steps. A new Fourier-BesselExpand
A discrete random walk on the hypercube
Abstract In this paper, we study the scaling for mean first-passage time (MFPT) of random walks on the hypercube and obtain a closed-form formula for the MFPT over all node pairs. We also determineExpand
Random Walks in the Plane
We study the expected distance of a two-dimensional walk in the plane with unit steps in random directions. A series evaluation and recursions are obtained making it possible to explicitly formulateExpand
On the problem of random flights
(The subsequent events and the solution are discussed in Sections 3 and 4.) This problem, which is basically concerned with the probability density of a sum of two-dimensional random vectors, wasExpand
Random walkers illuminate a math problem
  • H. Hill
  • Computer Science
  • Physics Today
  • 2019
A family of tricky integrals can now be solved without explicit calculation without any need for explicit calculation. Expand
The Pearson random walk with unequal step sizes
There have been many analyses of Pearson random walks with equal step sizes. Several applications suggest the importance of these walks with unequal step sizes. Numerical comparisons are made ofExpand
A Direct Proof of Significant Directed Random Walk
An equation is formed to enhance the connectivity of nodes in directed graph via weigh and the adjacency matrix is further enhances to increases the accessibility of nodes via vector. Expand
Lattice covering by two random walkers in one dimension
We study the average time necessary for two independent random walkers to cover a periodic one-dimensional lattice completely, as function of the lattice size and the starting positions of theExpand
Half-normal approximation for statistics of symmetric simple random walk
ABSTRACT In 2013, Döbler used Stein’s method to obtain the uniform bounds in half-normal approximation for three statistics of a symmetric simple random walk; the maximum value, the number of returnsExpand
Symmetric simple random walks
Random walks denote a general class of stochastic processes for which the definition significantly varies across the literature. Since the ultimate target of this textbook is spatial stochasticExpand