The Critical 2d Stochastic Heat Flow and Related Models

Autor:	Caravenna, Francesco, Sun, Rongfeng, Zygouras, Nikos
Rok vydání:	2024
Předmět:	Mathematics - Probability Mathematical Physics Primary: 82B44 Secondary: 35R60 60H15 82D60
Druh dokumentu:	Working Paper
Popis:	In these lecture notes, we review recent progress in the study of the stochastic heat equation and its discrete analogue, the directed polymer model, in spatial dimension 2. It was discovered that a phase transition emerges on an intermediate disorder scale, with Edwards-Wilkinson (Gaussian) fluctuations in the sub-critical regime. In the critical window, a unique scaling limit has been identified and named the critical 2d stochastic heat flow. This gives a meaning to the solution of the stochastic heat equation in the critical dimension 2, which lies beyond existing solution theories for singular SPDEs. We outline the proof ideas, introduce the key ingredients, and discuss related literature on disordered systems and singular SPDEs. A list of open questions is also provided. Comment: 70 pages, 7 figures. Lecture notes from courses given at Fondazione CIME, Peking University and Seoul National University
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.10311 Zobrazit plný text záznamu View this record from Arxiv