**Title:** The anchored expansion constant of random graphs

**Speaker:** Professor Dayue Chen

**Speaker Info:** Peking University

**Brief Description:**

**Special Note**:

**Abstract:**

This talk is based on my joint work with Yuval Peres and Gabor Pete of the University of California, Berkeley. The paper entitled "Anchored Expansion, Percolation and Speed" just appeared in the Annals of Probability.The anchored expansion constant is a variant of the Cheeger constant; its positivity implies positive lower speed for the simple random walk, as shown by Virag (2000). We prove that if G has a positive anchored expansion constant then so does every infinite cluster of independent percolation with parameter p sufficiently close to 1. We also show that positivity of the anchored expansion constant is preserved under a random stretch if, and only if, the stretching law has an exponential tail.

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