LLN and CLT in high dimensions for the random walk on the symmetric exclusion process
Date(s) : 24/06/2025 iCal
14h30 - 15h30
The random walk on the exclusion process is an example of random walk in
dynamic environment. In this specific model, the law of the movement of the
walker depends on whether its current position is occupied by a particle or
not. Furthermore, the position of the particles is given by a symmetric
exclusion process (on $\Z^d$). While this dynamic is quite simple, it has
the inconvenient of being both conservative and slowly mixing which will
cause strong correlations in the position of the particles. In dimension 1,
thanks to a monotonicity property, the model is somewhat well understood
but in higher dimensions only perturbative results are known. For a wide
range of parameters, we show that the walker satisfies a law of large
number in dimensions 5 and higher and a CLT in dimensions 9 and higher. For
this we look at the law of the environment knowing the trajectory of the
walker and show that it is not too far from the initial measure, for any
trajectory and conclude with standard tools for Markov chains.
Joint work with Guillaume Conchon-Kerjan and Daniel Kious.
Emplacement
I2M Saint-Charles - Salle de séminaire
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