國立清華大學 數學系

Abstract：The heat equation plays a fundamental role in probability theory through its close connection with diffusion processes. The classical heat flow is described by the convolution of an initial distribution with a Gaussian of increasing variance. Recent decades have seen the emergence of generalized probability theories, such as free probability, rectangular free probability, and finite free probability, in which different objects play the role of the convolution and the Gaussian distribution. Accordingly, each such theory gives rise to its own notion of "heat flow." This talk will explore the similarities and differences between these various conceptions of "heat," illustrating the wide range of ways to think about what the heat flow is and where it comes from.