Ornstein—Zernike theory for the near-critical planar random cluster model
Date(s) : 27/01/2026 iCal
14h30 - 15h30
In this talk, we will discuss the classical Ornstein-Zernike theory
for the random-cluster model (also known as FK percolation).
In its modern form, it is a very robust theory,
which most celebrated output is the computation
of the asymptotically polynomial corrections
to the pure exponential decay of the two-points correlation function
of the random-cluster model in the subcritical regime.
We will present a recent work
that extends this theory to the near-critical regime
of the two-dimensional random-cluster model,
thus providing a precise understanding of the Ornstein-Zernike asymptotics
when $p$ approaches the critical parameter $p_c$.
The output of this work is a formula
encompassing both the critical behaviour of the system
when looked at a scale negligible with respect to its correlation length,
and its subcritical behaviour
when looked at a scale way larger than its correlation length.
Based on a joint work with Ioan Manolescu.
Emplacement
I2M Saint-Charles - Salle de séminaire
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