Phase transition in random contingency tables with non-uniform margins

2019/03/20 by Sam Dittmer, Dittmer, Sam, Hanbaek Lyu +3
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistics Theory (math.ST) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1903.08743

openalex publication_date 2019/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For parameters n,δ,B, and C, let X=(X_kℓ) be the random uniform contingency table whose first \lfloor n^δ \rfloor rows and columns have margin \lfloor BCn \rfloor and the last n rows and columns have margin \lfloor Cn \rfloor. For every 0B_c. Our main result shows that 𝔼[X₁₁] 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.

Citations

• Algebraic algorithms for sampling from conditional distributions

Related

• On Properties of Random Binary Contingency Tables with Non-Uniform Margin
• Large random matrices with given margins
• On the number of contingency tables and the independence heuristic
• Asymptotic Enumeration of Binary Contingency Tables and Comparison with Independence Heuristic
• A Short Note on Asymptotic Enumeration of Contingency Tables with Non-Uniform Margins