Transience of conditioned walks on the plane: encounters and speed of escape
Serguei Popov, Leonardo T. Rolla, Daniel Ungaretti
Abstract
We consider the two-dimensional simple random walk conditioned on never hitting the origin, which is, formally speaking, the Doob’s $h$-transform of the simple random walk with respect to the potential kernel. We then study the behavior of the future minimum distance of the walk to the origin, and also prove that two independent copies of the conditioned walk, although both transient, will nevertheless meet infinitely many times a.s.
Topics & Concepts
MathematicsRandom walkSimple (philosophy)Simple random sampleHeterogeneous random walk in one dimensionLoop-erased random walkHitting timeStatistical physicsCombinatoricsDiscrete mathematicsLarge deviations theoryStochastic processes and statistical mechanicsDiffusion and Search DynamicsRandom Matrices and Applications