Probability Seminar
Day, Date and Time : Thursday 26th Sept 3:00 pm
Venue : Ramanujan Hall
Speaker : Parthanil Roy
Title : Detailed Analysis of Phase Transition for Elephant Random Walks
with Two Memory Channels
Abstract : Random processes with strong memory and/or self-excitation
arise naturally in various disciplines including physics, economics,
biology, engineering, geology, etc. Memory can be multifaceted and can
arise due to interactions of more than one underlying phenomena. Many of
these processes exhibit superdiffusive growth due to the effect of
self-excitation. A class of one-dimensional, discrete-time such models
called “elephant random walk with n memory channels” was introduced and
discussed in a recent paper on statistical physics by Saha (2022). In
these models the information of n previous steps from the walker’s entire
history is needed to decide the future step. The aforementioned work
carried out a bunch of calculations, and conjectured a phase transition
from diffusive to superdiffusive regime based on some numerical
computations in the n=2 case. We have been able to prove these conjectures
rigorously and establish a few new transition boundaries beyond the
predicted ones. I shall present these results along with several open
problems. (This talk is based on a joint work with Krishanu Maulik and
Tamojit Sadhukhan.)