MATH 7710 FALL 2020

Topics in Probability: Abelian Networks and Activated Random Walk

Lionel Levine

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October 22: Jacob Richey

Jacob told us about his proof with Hoffman and Rolla that the critical density $\zeta_c(\lambda)$ for Activated Random Walk on $\mathbb{Z}$ is strictly less than one for any sleep rate $\lambda<\infty$ . Paper: https://arxiv.org/abs/2009.09491 (A key point the proof is Lemma 4.3!)

October 22, 2020

October 20: Leonardo Rolla

Leo told us about the phase diagram between Activity and Fixation for Activated Random Walk in $\mathbb{Z}^d$ : what’s conjectured and what’s known. A useful tool is the equivalence between site fixation and particle fixation, proved by Amir and Gurel-Gurevich in this short sweet paper.

October 20, 2020

October 15: Ask me anything!

Today’s class will be an AMA “Ask Me Anything”. Reply to this post with a question and I will answer it in class!

October 15, 2020

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