確率論セミナー


2019/1/15(Tue)

16:30--18:00 数学教室 大セミナー室 (E404)

篠田 万穂

慶應義塾大学

A locally constant function without zero temperature limit

We consider the sequence of equilibrium measures in the context of symbolic dynamical systems. Parametrizing the equilibrium measures by temperature, we pay attention to the behavior of the sequence when the temperature dropes to zero. More precisely, we discuss convergence and non-convergence. In the one-dimensional case, for a locally constant function the sequence of equilibrium measures converges. However in the high-dimensional case, there exists a locally constant function whose sequence of equilibrium measures does not converge. We construct such a locally constant function in dimension two by imbedding a one-dimensional effective subshift into a two-dimensional subshift of finite type. This is a joint work with Jean-Rene Chazottes in Ecole Polytechnique.