Seminar Event Detail


Date:  Friday, January 26, 2018
Location:  4088 East Hall (4:10 PM to 5:00 PM)

Title:  Double jump phase transition in a random soliton cellular automaton

Abstract:   In this work, we consider the soliton cellular automaton introduced in cite{takahashi1990soliton} with a random initial configuration. We give multiple constructions of a Young diagram describing various statistics of the system in terms of familiar objects like birth-and-death chains and Galton-Watson forests. Using these ideas, we establish limit theorems showing that if the first $n$ boxes are occupied independently with probability $pin(0,1)$, then the number of solitons is of order $n$ for all $p$, and the length of the longest soliton is of order $log n$ for $p<1/2$, order $sqrt{n}$ for $p=1/2$, and order $n$ for $p>1/2$. Additionally, we uncover a condensation phenomenon in the supercritical regime: For each fixed $jgeq 1$, the top $j$ soliton lengths have the same order as the longest for $pleq 1/2$, whereas all but the longest have order at most $log n$ for $p>1/2$. As an application, we obtain scaling limits for the lengths of the $k^{ ext{th}}$ longest increasing and decreasing subsequences in a random stack-sortable permutation of length $n$ in terms of random walks and Brownian excursions.


Speaker:  Hanbaek Lyu
Institution:  Ohio State U.

Event Organizer:     


Edit this event (login required).
Add new event (login required).
For access requests and instructions, contact

Back to previous page
Back to UM Math seminars/events page.