Survival probability of stochastic processes beyond persistence exponents
VOITURIEZ, R.
Laboratoire de Physique Théorique de la Matière Condensée [LPTMC]
Laboratoire Jean Perrin [LJP]
< Reduce
Laboratoire de Physique Théorique de la Matière Condensée [LPTMC]
Laboratoire Jean Perrin [LJP]
Language
en
Article de revue
This item was published in
Nature Communications. 2019-12, vol. 10, n° 1, p. 2990 (2019)
Nature Publishing Group
English Abstract
For many stochastic processes, the probability S(t) of not-having reached a target in unbounded space up to time t follows a slow algebraic decay at long times, S(t)∼S0/tθ. This is typically the case of symmetric compact ...Read more >
For many stochastic processes, the probability S(t) of not-having reached a target in unbounded space up to time t follows a slow algebraic decay at long times, S(t)∼S0/tθ. This is typically the case of symmetric compact (i.e. recurrent) random walks. While the persistence exponent θ has been studied at length, the prefactor S0, which is quantitatively essential, remains poorly characterized, especially for non-Markovian processes. Here we derive explicit expressions for S0 for a compact random walk in unbounded space by establishing an analytic relation with the mean first-passage time of the same random walk in a large confining volume. Our analytical results for S0 are in good agreement with numerical simulations, even for strongly correlated processes such as Fractional Brownian Motion, and thus provide a refined understanding of the statistics of longest first-passage events in unbounded space.Read less <
English Keywords
Chemical physics
Statistical physics
Origin
Hal imported