Continuum polymer measures corresponding to the critical 2d stochastic heat flow

Autor:	Clark, Jeremy, Mian, Barkat
Rok vydání:	2024
Předmět:	Mathematics - Probability 82B44 35R60 82D60 60H15 60G57
Druh dokumentu:	Working Paper
Popis:	We construct continuum directed polymer measures corresponding to the critical 2d stochastic heat flow (2d SHF) introduced by Caravenna, Sun, and Zygouras in their recent article [Inventiones mathematicae 233, 325--460 (2023)]. For this purpose, we prove a Chapman-Kolmogorov relation for the 2d SHF along with a related elementary conditional expectation formula. We explore some basic properties of the continuum polymer measures, with our main focus being on their second moments. In particular, we show that the form of their second moments is consistent with the family of continuum polymer measures, indexed by a disorder strength parameter, having a conditional Gaussian multiplicative chaos distributional interrelationship similar to that previously found in an analogous hierarchical toy model. Comment: 39 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.01510 Zobrazit plný text záznamu View this record from Arxiv