Related papers: On Properties of Random Binary Contingency Tables …

Let $C\geq 2$ be a positive integer. Consider the set of $n\times n$ non-negative integer matrices whose row sums and column sums are all equal to $Cn$ and let $X=(X_{ij})_{1\leq i,j\leq n}$ be uniformly distributed on this set. This $X$ is…

In this short note, we compute the precise asymptotics for the number of contingency tables with non-uniform margins. More precisely, for parameter $n,\delta, B,C>0$, we consider the set of matrices whose first $[n^\delta]$ rows and columns…

For parameters $n,\delta,B,$ and $C$, let $X=(X_{k\ell})$ 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…

A binary contingency table is an m x n array of binary entries with prescribed row sums r=(r_1,...,r_m) and column sums c=(c_1,...,c_n). The configuration model for uniformly sampling binary contingency tables proceeds as follows. First,…

We consider the asymptotic distribution of a cell in a 2 x ... x 2 contingency table as the fixed marginal totals tend to infinity. The asymptotic order of the cell variance is derived and a useful diagnostic is given for determining…

For parameters $n,\delta,B,C$, we obtained a sharp asymptotic formula for the number of $(n+\lfloor n^\delta\rfloor)^2$-dimensional binary contingency tables with non-uniform margins taking values of $\lfloor BCn\rfloor$ and $\lfloor…

Let R=(r_1, ..., r_m) and C=(c_1, ..., c_n) be positive integer vectors such that r_1 +... + r_m=c_1 +... + c_n. We consider the set Sigma(R, C) of non-negative mxn integer matrices (contingency tables) with row sums R and column sums C as…

We study the problem of transforming a multi-way contingency table into an equivalent table with uniform margins and same dependence structure. Such a problem relates to recent developments in copula modeling for discrete random vectors.…

We construct examples of contingency tables on $n$ binary random variables where the gap between the linear programming lower/upper bound and the true integer lower/upper bounds on cell entries is exponentially large. These examples provide…

We study the problem of transforming a multi-way contingency table into an equivalent table with uniform margins and same dependence structure. This is an old question which relates to recent advances in copula modeling for discrete random…

We determine the asymptotic number of regular multipartite hypergraphs, also known as multidimensional binary contingency tables, for all values of the parameters.

In this paper we consider a Bayesian analysis of contingency tables allowing for the possibility that cells may have probability zero. In this sense we depart from standard log-linear modeling that implicitly assumes a positivity…

By means of a binary visibility graph, we present a novel method to study random binary sequences. The behavior of the some topological properties of the binary visibility graph, such as the degree distribution, the clustering coefficient,…

The main goal of this paper is to determine the asymptotic behavior of the number $X_n$ of cut-vertices in random planar maps with $n$ edges. It is shown that $X_n/n \to c$ in probability (for some explicit $c>0$). For so-called subcritical…

We study the behavior of configurations in the symmetric six-vertex model with $a,b,c$ weights in the $n\times n$ square with Domain Wall Boundary Conditions as $n\to\infty$. We prove that when $\Delta=\frac{a^2+b^2-c^2}{2ab}<1$,…

We investigate the number of symmetric matrices of non-negative integers with zero diagonal such that each row sum is the same. Equivalently, these are zero diagonal symmetric contingency tables with uniform margins, or loop-free regular…

We study non-compact scaling limits of uniform random planar quadrangulations with a boundary when their size tends to infinity. Depending on the asymptotic behavior of the boundary size and the choice of the scaling factor, we observe…

We study the geometric structure of the statistical models for two-by-two contingency tables. One or two odds ratios are fixed and the corresponding models are shown to be a portion of a ruled quadratic surface or a segment. Some pointers…

Motivated by applications to perverse sheaves, we study combinatorics of two cell decompositions of the symmetric product of the complex line, refining the complex stratification by multiplicities. Contingency matrices, appearing in…

Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…