Lionel Levine

How do simple local interactions combine to produce complex large-scale structure and patterns? The abelian sandpile model provides a beautiful test case. I'll discuss a pair of conjectures about the scale invariance and dimensional reduction of the...

How do simple local interactions combine to produce complex large-scale structure and patterns? The abelian sandpile model provides a beautiful test case. I'll discuss a pair of conjectures about the scale invariance and dimensional reduction of the...

Start with n particles at the origin in the square grid Z2, and let each particle in turn perform simple random walk until reaching an unoccupied site. Lawler, Bramson and Griffeath proved that with high probability the resulting random set of n...

I will describe the role played by an Apollonian circle packing in the scaling limit of the abelian sandpile on the square grid Z^2. The sandpile solves a certain integer optimization problem. Associated to each circle in the packing is a locally...

The 18th Northwest Probability Seminar, a one-day mini-conference organized by the University of Washington, the Oregon State University, the University of British Columbia, the University of Oregon, and the Theory Group at Microsoft Research, will...