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Thursday, 11 September, 10:09, sergepolar.livejournal.com
http://arxiv.org/abs/1409.2907
Slow Death by Many Mosquito Bites
S. Redner, O. Bénichou
(Submitted on 9 Sep 2014)

We study the dynamics of a single diffusing particle (a "man") with diffusivity that is attacked by another diffusing particle (a "mosquito") with fixed diffusivity . Each time the mosquito meets and bites the man, the diffusivity of the man is reduced by a fixed amount, while the diffusivity of the mosquito is unchanged. The mosquito is also displaced by a small distance with respect to the man after each encounter. The man is defined as dead when reaches zero. At the moment when the man dies, his probability distribution of displacements is given by a Cauchy form, which asymptotically decays as , while the distribution of times when the man dies asymptotically decays as , which has the same form as the one-dimensional first-passage probability.

Comments: 10 pages, 2 figure, IOP format


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