Random walk theory of a trap-controlled hopping transport process

A Random Walk with Exponential Travel Times

Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...

Controlled random walk with a target site ∗

We consider a symmetric simple random walk {Wi} on Z, d = 1, 2, in which the walker may choose to stand still for a limited time. The time horizon is n, the maximum consecutive time steps which can be spent standing still is mn and the goal is to maximize P (Wn = 0). We show that for d = 1, if mn (logn) for some γ > 0, there is a strategy for each n yielding P (Wn = 0) → 1. For d = 2, if mn n f...

Testing the Random-Walk Theory

Scaling of a random walk on a supercritical contact process

A proof is provided of a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof is based on a coupling argument that traces the space-time cones containing the infection clusters generated by single infections and uses that the random walk eventually gets trapped inside the union of these c...

Intracellular transport of insulin granules is a subordinated random walk.

We quantitatively analyzed particle tracking data on insulin granules expressing fluorescent fusion proteins in MIN6 cells to better understand the motions contributing to intracellular transport and, more generally, the means for characterizing systems far from equilibrium. Care was taken to ensure that the statistics reflected intrinsic features of the individual granules rather than details ...