Thermalisation for small random perturbations of dynamical systems

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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.
TidskriftAnnals of Applied Probability
Sidor (från-till)1164-1208
Antal sidor45
StatusPublicerad - jun 2020
MoE-publikationstypA1 Tidskriftsartikel-refererad


  • 111 Matematik
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