演講訊息 TALKS

Self-avoiding walk (SAW) on $\mathbb{Z}^d$ is often used as a model for linear polymers in $d$ dimensions. It is known that the susceptibility ( = the sum of the two-point function) diverges as the energy-cost $h$ for each bond goes down to the critical point $-\log\mu$, where $\mu$ is the connective constant. Suppose that the energy-cost is not homogeneous, but it is perturbed by i.i.d. random variables, so that the susceptibility becomes random and loses translation invariance. A natural question would be to ask how the randomness affects the phase transition and critical behavior of SAW. In the talk, I will explain the recent results on the quenched critical point and future problems.