Séminaire des jeunes chercheurs

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Intervenant : MASSOULIÉ Brune (CEREMADE)
Titre :
Cutoff for the mixing time of the facilitated exclusion process

Le : 27/03/2025 de : 17:00 à : 18:00
The facilitated exclusion process (FEP) is a particle system, where particles evolve on a discrete lattice, making random jumps while obeying local constraints. Its evolution rules mean that some zones are frozen while others have movement, thus modelling a liquid-solid interface. After a transience time, it is either completely frozen or reaches an ergodic component. We estimated this transience time, using a mapping to another process, the SSEP with traps. When the FEP doesn’t freeze and continues moving, one can study its mixing time, meaning the time needed to be close to equilibrium. The cutoff phenomenon is the very abrupt decrease of the distance to equilibrium with time, and has been observed in many Markov chains, the historical example being card shufflings. We prove cutoff for the mixing time of the FEP, by showing the time spent in the transient phase and the ergodic phase balance each other out.
Salle : A707