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2 results

  • Deviation bounds for the first passage time in the frog model

  • Part of
  • Naoki Kubota
  • Journal:
    Advances in Applied Probability / Volume 51 / Issue 1 / March 2019
    Published online by Cambridge University Press:
    22 July 2019, pp. 184-208
    Print publication:
    March 2019

  • We consider the so-called frog model with random initial configurations. The dynamics of this model are described as follows. Some particles are randomly assigned to any site of the multidimensional cubic lattice. Initially, only particles at the origin are active and these independently perform simple random walks. The other particles are sleeping and do not move at first. When sleeping particles are hit by an active particle, they become active and start moving in a similar fashion. The aim of this paper is to derive large deviation and concentration bounds for the first passage time at which an active particle reaches a target site.

  • A simple random walk on parallel axes moving at different rates

  • V. Barnett
  • Journal:
    Journal of Applied Probability / Volume 12 / Issue 3 / September 1975
    Published online by Cambridge University Press:
    14 July 2016, pp. 466-476
    Print publication:
    September 1975

  • Prompted by a rivulet model for the flow of liquid through packed columns we consider a simple random walk on parallel axes moving at different rates. A particle may make one of three transitions at each time instant: to the right or to the left on the axis it was on at the previous time instant, or across to the other axis. Results are obtained for the unrestricted walk, and for the walk with absorbing, or reflecting, end-points.