RANDOM WALK, SCATTERING, AND INVARIANT IMBEDDING I. ONE-DIMENSIONAL DISCRETE CASE

Random Walk, Scattering, and Invariant Imbedding I. One-dimensional Discrete Case.

O < Random Walk , Scatterino and Invariant Imbeddino — I : One - Dimensional Discrete Case

Dissipation Functions and Invariant Imbedding, I.

Erosion by a one-dimensional random walk.

We consider a model introduced by Baker et al. [Phys. Rev. E 88, 042113 (2013)] of a single lattice random walker moving on a domain of allowed sites, surrounded by blocked sites. The walker enlarges the allowed domain by eroding the boundary at its random encounters with blocked boundary sites: attempts to step onto blocked sites succeed with a given probability and convert these sites to allo...

Tail estimates for one-dimensional random walk in random environment

Suppose that the integers are assigned i.i.d. random variables f! x g (taking values in the unit interval), which serve as an environment. This environment deenes a random walk fX k g (called a RWRE) which, when at x, moves one step to the right with probability ! x , and one step to the left with probability 1 ? ! x. Solomon (1975) determined the almost-sure asymptotic speed (=rate of escape) ...