Publications [#371967] of Alexander J Dunlap

Papers Published

1. Dunlap, A; Gu, Y; Li, L, Localization length of the $1+1$ continuum directed random polymer, Annales Henri Poincaré, vol. 24 no. 7 (July, 2023), pp. 2537-2555, Springer Science and Business Media LLC [doi]
   (last updated on 2024/07/16)

   Abstract:
   In this paper, we study the localization length of the continuum directed polymer, defined as the distance between the endpoints of two paths sampled independently from the quenched polymer measure. We show that the localization length converges in distribution in the thermodynamic limit, and derive an explicit density formula of the limiting distribution. As a consequence, we prove the $\frac32$-power law decay of the density, confirming the physics prediction of Hwa and Fisher (Phys Rev B 49(5):3136, 1994). Our proof uses the recent result of Das and Zhu (Localization of the continuum directed random polymer, 2022).