LEVERNIER, N.; DOLGUSHEV, M.; BENICHOU, O.; VOITURIEZ, R.; GUÉRIN, T.

doi:10.1038/s41467-019-10841-6

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LEVERNIER, N.

DOLGUSHEV, M.
Laboratoire de Physique Théorique de la Matière Condensée [LPTMC]

BENICHOU, O.
Laboratoire de Physique Théorique de la Matière Condensée [LPTMC]

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Nature Communications. 2019-12, vol. 10, n° 1, p. 2990 (2019)

Nature Publishing Group

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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.< Réduire

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Chemical physics

Statistical physics

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Survival probability of stochastic processes beyond persistence exponents

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