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UID:8946@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20260303T143000
DTEND;TZID=Europe/Paris:20260303T153000
DTSTAMP:20260122T132229Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-277/
SUMMARY:Francesca Cottini (Sorbonne Université): Directed polymer in corre
 lated environment
DESCRIPTION:Francesca Cottini: Directed polymers in random environments des
 cribe a perturbation of the simple random walk given by a random disorder 
 (environment). The partition functions of this model have been thoroughly 
 investigated in recent years\, also motivated by their link with the solut
 ion of the Stochastic Heat Equation. While classical results focus on spac
 e-time independent disorder\, we consider a Gaussian environment with (cri
 tical) spatial correlations decaying as $|x|^{-2}$ times a slowly varying 
 function. We show that a phase transition\, analogous to that in the space
 -time independent case\, still occurs: in the high temperature regime the 
 log-partition function satisfies a central limit theorem\, while it vanish
 es in law in the low temperature regime. Remarkably\, the inverse temperat
 ure needs to be tuned differently from the independent case\, where the sc
 aling constant $\\hat{\\beta}$ emerges from a nontrivial multi-scale depen
 dence in the second moment computation — the core technical challenge of
  the work. Based on a joint work with Clément Cosco (Paris Dauphine) and 
 Anna Donadini (Milano-Bicocca).
CATEGORIES:Séminaire,ALEA,Probabilités
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\,
  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
 -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0
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