Thermalisation for small random perturbations of dynamical systems

Tutkimustuotos: ArtikkelijulkaisuArtikkeliTieteellinenvertaisarvioitu

Abstrakti

We consider an ordinary differential equation with a unique hyperbolic
attractor at the origin, to which we add a small random perturbation. It is
known that under general conditions, the solution of this stochastic differential
equation converges exponentially fast to an equilibrium distribution. We
show that the convergence occurs abruptly: in a time window of small size
compared to the natural time scale of the process, the distance to equilibrium
drops from its maximal possible value to near zero, and only after this time
window the convergence is exponentially fast. This is what is known as the
cut-off phenomenon in the context of Markov chains of increasing complexity.
In addition, we are able to give general conditions to decide whether the
distance to equilibrium converges in this time window to a universal function,
a fact known as profile cut-off.
Alkuperäiskielienglanti
LehtiAnnals of Applied Probability
Vuosikerta30
Numero3
Sivut1164-1208
Sivumäärä45
ISSN1050-5164
DOI - pysyväislinkit
TilaJulkaistu - kesäk. 2020
OKM-julkaisutyyppiA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä, vertaisarvioitu

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