Generalized Ray-Knight theorems: their applications and limitations

Organizers：

吴昊，杨帆，姜建平，顾陈琳

Speaker：

Elena Kosygina (NYU Shanghai and CUNY)

Time：

Thur., 3:40-4:40 pm, Nov. 28, 2024

Venue：

C548, Shuangqing Complex Building A

Title：

Generalized Ray-Knight theorems: their applications and limitations

Abstract:

For several classes of self-interacting random walks on the integers, the generalized Ray-Knight theorems serve as the main tool for finding a candidate for a scaling limit and proving the convergence to that limiting process. A natural question to ask is whether theorems are not just a tool but whether, in fact, they uniquely identify the limiting process and, under some mild conditions, imply convergence. Recently, in a joint work with T. Mountford and J. Peterson, we showed that this need not be the case in general, and more information is needed to imply convergence. This negative answer prompted the follow-up question: would the joint generalized Ray-Knight theorems suffice for the task? In our ongoing project, we explore this idea for two classes of self-interacting random walks that were introduced and studied by B. Tóth in 1995-96.