DATE2022-05-05 16:10-17:00

PLACE數學系館 1F3174教室

SPEAKER黃建豪 博士(國立政治大學應用數學系

TITLEThe Statistical Mechanics of Wiener Sausages

We first discuss one basic idea in mathematical statistical mechanics: large deviations. Secondly, we review the materials in the theory of random walks. Physicists and mathematicians use those concepts to discuss phase transitions in polymer models. In this talk, the directed polymer model is the statistical mechanics model with the hamiltonian described by the d-dimensional random walk in space-time random environments. The particles gain energy whenever they visit the potential sites. The analogous continuum model, namely, the model with noise formally defined on R^d, which is the stochastic heat equation with space-time white noise, is not well-defined. Recently many discussions on it. We propose a new model that the particles only gain energy at their first visit with the noise being independent of time. In the continuum and weak disorder regime, the partition function of our model as a random variable converges weakly to a Wiener Chaos expansion, however, it describes a different phenomenon.