DELTA-BOSE GAS FROM THE VIEWPOINT OF THE TWO-DIMENSIONAL STOCHASTIC HEAT EQUATION

• 成果类型: Article
• 署名作者: Hen, Yu-Ting
• 署名单位: University of Victoria
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/23-AOP1649
• 发表日期: 2024
• 页码: 127-187
• 关键词: point interactions; systems

摘要

In order to give a dual, annealed description of the two-dimensional stochastic heat equation (SHE) from regularizing the noise, we consider the Schrodinger semigroup of the many -body delta -Bose gas from mollifying the delta potentials. The main theorem proves the convergences of the corresponding approximate semigroups when they act on bounded functions. For the proof we introduce a mean -field Poisson system to expand the Feynman- Kac formula of the approximate semigroups. This expansion yields infinite series, showing certain Markovian decompositions of the summands into nonconcurrent, nonconsecutive two -body interactions. Components in these decompositions are then grouped nonlinearly in time to establish the dominated convergence of the infinite series. With regards to the two-dimensional SHE, the main theorem also characterizes the Nth moments for all N >= 3 under any bounded initial condition. A particular example is the constant initial condition under which the solution of the SHE has the interpretation of the partition function of the continuum directed random polymer.