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- W1489491188 abstract "We consider bridges for the simple exclusion process on Z, either symmetric or asymmetric, in which particles jump to the right at rate p and to the left at rate 1 − p. The initial state O has all negative sites occupied and all nonnegative sites empty. We study the probability that the process is again in state O at time t, and the behaviour of the process on [0,t] conditioned on being in state O at time t. In the case p = 1/2, we find that such a bridge typically goes a distance of order t (in the sense of graph distance) from the initial state. For the asymmetric systems, p 6 1/2, we note an interesting duality which shows that bridges with parameters p and 1 − p have the same distribution; the maximal distance of the process from the original state behaves like c(p)logt for some constant c(p) depending on p. (For p > 1/2, the front particle therefore travels much less far than the bridge of the corresponding random walk, even though in the unconditioned process the path of the front particle dominates a random walk.) We mention various further questions." @default.
- W1489491188 created "2016-06-24" @default.
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- W1489491188 date "2012-03-01" @default.
- W1489491188 modified "2023-09-27" @default.
- W1489491188 title "How to squeeze the toothpaste back into the tube" @default.
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