**Algorithms & Randomness Center (ARC) **

**Antonio Blanca - UC Berkeley**

**Friday, February 5, 2016**

**Klaus 1116 East (not West) - 2:00 pm**

**(Refreshments will be served in Klaus 2222 at 3 pm)**

**Title: **Dynamics for the random-cluster model

**Abstract:**

The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and electrical networks, but its dynamics have so far largely resisted analysis. In this talk we present recent results concerning the mixing behavior of natural Markov chains for the random-cluster model in two canonical cases: the mean-field model and the two dimensional lattice graph Z^2. In the mean-field case, we identify a critical regime of the model parameter p in which several natural dynamics undergo an exponential slowdown. In Z^2, we provide tight mixing time bounds for the heat-bath dynamics for all non-critical values of p. These results hold for all values of the second model parameter q > 1.

Based on joint works with Alistair Sinclair.

Short Bio: Antonio Blanca is a 5th year PhD student at UC Berkeley advised by Alistair Sinclair. He is interested in algorithms, Markov chain mixing, phase transitions and random structures. He graduated with a BS in Computer Science/Discrete Math from Georgia Tech.

denton at cc dot gatech dot edu

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