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We study the excited random walk, in which a walk that is at a site that contains cookies eats one cookie and then hops to the right with probability p and to the left with probability q = 1 − p. If the walk hops onto an empty site, there is no bias. For the 1-excited walk on the half-line (one cookie initially at each site), the probability of first(More)
PACS 98.80.-k – Cosmology PACS 05.40.-a – Fluctuations phenomena in random processes PACS 02.50.-r – Probability theory, stochastic processes, and statistics Abstract.-We consider the conditional galaxy density around each galaxy, and study its fluctuations in the newest samples of the Sloan Digital Sky Survey Data Release 7. Over a large range of scales,(More)
An explicit solution for a general two-type birth-death branching process with one way mutation is presented. This continuous time process mimics the evolution of resistance to treatment, or the onset of an extra driver mutation during tumor progression. We obtain the exact generating function of the process at arbitrary times, and derive various large time(More)
We study a two-type branching process which provides excellent description of experimental data on cell dynamics in skin tissue (Clayton et al., 2007). The model involves only a single type of progenitor cell, and does not require support from a self-renewed population of stem cells. The progenitor cells divide and may differentiate into post-mitotic cells.(More)
We solve the problem of discrete translocation of a polymer through a pore, driven by the irreversible, random sequential adsorption of particles on one side of the pore. Although the kinetics of the wall motion and the deposition are coupled, we find the exact steady-state distribution for the gap between the wall and the nearest deposited particle. This(More)
We study the first-passage properties of a random walk in the unit interval in which the length of a single step is uniformly distributed over the finite range [−a, a]. For a of the order of one, the exit probabilities to each edge of the interval and the exit time from the interval exhibit anomalous properties stemming from the change in the minimum number(More)
Synthetic bio-molecular spiders with " legs " made of single-stranded segments of DNA can move on a surface covered by single-stranded segments of DNA called substrates when the substrate DNA is complementary to the leg DNA. If the motion of a spider does not affect the substrates, the spider behaves asymptotically as a random walk. We study the diffusion(More)
We study a directed flipping process that underlies the performance of the random edge simplex algorithm. In this stochastic process, which takes place on a one-dimensional lattice whose sites may be either occupied or vacant, occupied sites become vacant at a constant rate and simultaneously cause all sites to the right to change their state. This random(More)