We consider the endpoint large deviation for a continuous-time directed polymer in a Lévy-type random environment. When the space dimension is at least three, it is known that the so-called weak disorder phase exists, where the quenched and annealed free energies coincide. We prove that the rate function agrees with that of the underlying random walk near the origin in the whole interior of the weak disorder phase.
RF is supported by ISHIZUE 2019 of Kyoto University Research Development Program. SJ is supported by a JSPS Postdoctoral Fellowship for Research in Japan, Grant-in-Aid for JSPS Fellows 19F19814. This work was supported by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.
"On large deviation rate functions for a continuous-time directed polymer in weak disorder." Electron. Commun. Probab. 26 1 - 10, 2021. https://doi.org/10.1214/21-ECP378