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math.PR2025
A central limit theorem for two-dimensional directed polymers with critical spatial correlation
Clément Cosco, Francesca Cottini, Anna Donadini
On the 1+2 dimensional lattice, we consider a directed polymer in a random Gaussian environment that is independent in time and correlated in space. The spatial correlation is supp…
math.PR2025
The maximum of the two dimensional Gaussian directed polymer in the subcritical regime
Clément Cosco, Shuta Nakajima, Ofer Zeitouni
We study the maximum of the partition function of the two dimensional (subcritical) Gaussian directed polymer over an box. We show that $ϕ_N^*/\log…
math.PR2025
High moments of 2d directed polymers up to quasi-criticality
Clément Cosco, Shuta Nakajima
We consider two-dimensional directed polymers in random environment in the sub-critical regime and in the quasi-critical regime introduced recently by Caravenna, Cottini and Rossi,…