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### MULTIPLE PHASE TRANSITIONS FOR LONG-RANGE FIRST-PASSAGE PERCOLATION ON LATTICES

**Mathematical Physics & Probability**

Speaker: | Shirshendu Chatterjee, NYU |

Location: | 2112 MSB |

Start time: | Wed, Apr 10 2013, 4:10PM |

Given a graph G with non-negative edge weights, the passage time of a path is the sum of weights of the edges in the path, and the first-passage time to reach u from v is the minimum passage time of a path joining them. We consider a long range first-passage model on Zd in which, the weight w⟨xy⟩ of the edge joining x, y ∈ Zd has exponential distribution with mean ||x−y||α for some fixed α > 0, and the edge weights are independent. We analyze the growth of the set of vertices reachable from the origin within time t, and show that there are four different growth regimes depending on the value of α. Joint work with Partha Dey.