Date: Friday, September 27, 2019
Location: 4096 East Hall (3:00 PM to 4:00 PM)
Title: Phase transition in random contingency tables with nonuniform margins
Abstract: For parameters n,\delta,B, and C, let X=(X_{k\ell}) be the random uniform contingency table whose first n^{\delta} rows and columns have margin BCn and the last n rows and columns have margin Cn. For every 0<\delta<1, we establish a sharp phase transition of the limiting distribution of each entry of X at the critical value B_{c}=1+\sqrt{1+1/C}. In particular, for 1/2<\delta<1, we show that the distribution of each entry converges to a geometric distribution in total variation distance, whose mean depends sensitively on whether BB_{c}. Our main result shows that \E[X_{11}] is uniformly bounded for BB_{c}. We also establish a strong law of large numbers for the row sums in top right and top left blocks.
This is a joint work with Sam Dittmer and Igor Pak.
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Speaker: Hanbaek Lyu
Institution: UCLA
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