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Riddhipratim Basu (Stanford University, USA)
Date & Time
Thu, 22 December 2016, 10:30 to 11:30
Emmy Noether Seminar Room, ICTS Campus, Bangalore

Activated Random Walk, an interacting particle system with Abelian property, was introduced as an approximation of Manna's Stochastic Sandpile Model, a paradigm example of a model of self-organized criticality. On $\mathbb{Z}$, one starts with a mass density $\mu$ of active particles each of which independently performs a continuous time simple symmetric random walk at rate one and falls asleep at rate $\lambda>0$. Sleepy particles become active on coming in contact with active particles. As the model parameters vary, the system exhibits Absorbing State Phase Transition: it goes from reaching a state of fixation to a state where activity is sustained at all times. I shall describe a joint work with Shirshendu Ganguly and Christopher Hoffman showing non-fixation at arbitrarily small particle density provided the sleep rate $\lambda$ is sufficiently small. This answers two open questions posed by Dickman, Rolla and Sidoravicius in 2010.