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- W2925172351 abstract "For parameters $n,delta,B,$ and $C$, let $X=(X_{kell})$ be the random uniform contingency table whose first $lfloor n^{delta} rfloor $ rows and columns have margin $lfloor BCn rfloor$ and the last $n$ rows and columns have margin $lfloor Cn rfloor$. 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 $B<B_{c}$ or $B>B_{c}$. Our main result shows that $mathbb{E}[X_{11}]$ is uniformly bounded for $B<B_{c}$, but has sharp asymptotic $C(B-B_{c}) n^{1-delta}$ for $B>B_{c}$. We also establish a strong law of large numbers for the row sums in top right and top left blocks." @default.
- W2925172351 created "2019-04-01" @default.
- W2925172351 creator A5060457814 @default.
- W2925172351 creator A5065059104 @default.
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- W2925172351 date "2019-03-20" @default.
- W2925172351 modified "2023-09-26" @default.
- W2925172351 title "Phase transition in random contingency tables with non-uniform margins" @default.
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- W2925172351 doi "https://doi.org/10.48550/arxiv.1903.08743" @default.
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