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• W3013951715 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.
• W3013951715 created "2020-04-03" @default.
• W3013951715 creator A5060053636 @default.
• W3013951715 creator A5065059104 @default.
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• W3013951715 date "2020-10-05" @default.
• W3013951715 modified "2023-09-26" @default.
• W3013951715 title "Phase transition in random contingency tables with non-uniform margins" @default.
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• W3013951715 doi "https://doi.org/10.1090/tran/8094" @default.
• W3013951715 hasPublicationYear "2020" @default.
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