H. Lacoin

collaborators

8 papers

math.PR2025

Coincidence of critical points for directed polymers for general environments and random walks

Stefan Junk, Hubert Lacoin

For the directed polymer in a random environment (DPRE), two critical inverse-temperatures can be defined. The first one, $I^_{c}^{2}$ , separates the strong disorder regime (in which the…

math.PR2025

Strong disorder and very strong disorder are equivalent for directed polymers

Stefan Junk, Hubert Lacoin

We show that if the normalized partition function $W_{n}^{2}$ of the directed polymer model on $Z^{d}$ converges to zero, then it does so exponentially fast. This implies that t…

math.PR2025

The Random Walk Pinning Model I: Lower bounds on the free energy and disorder irrelevance

Quentin Berger, Hubert Lacoin

The Random Walk Pinning Model (RWPM) is a statistical mechanics model in which the trajectory of a continuous time random walk $X = (X_{t})_{t \geq 0}$ is rewarded according to the time…

math.PR2025

The Random Walk Pinning Model II: Upper bounds on the free energy and disorder relevance

Quentin Berger, Hubert Lacoin

This article investigates the question of disorder relevance for the continuous-time Random Walk Pinning Model (RWPM) and completes the results of our companion paper. The RWPM con…

math.PR2025

The localization transition for the directed polymer in a random environment is smooth

Hubert Lacoin

When $d \geq 3$ , the directed polymer a in random environment on $Z^{d}$ is known to display a phase transition from a diffusive phase, known as \textit{weak disorder} to a loc…

math.PR2025

A short proof of diffusivity for the directed polymers in the weak disorder phase

Hubert Lacoin

We provide a new short and elementary proof of diffusivity for directed polymer in a random environment in the weak disorder phase.