Here we solve N × N Riemann-Hilbert (inverse monodromy) problems with all monodromy matrices having the structure of matrices of quasi-permutation (i.e. matrices which have only one non-zero element in each column and each row). Such RiemannHilbert problem may be associated to arbitrary Hurwitz space of algebraic curves L of genus g realized as N -sheeted covering over CP1, and allowes solution...

We prove an asymptotic estimate for the number of m×n non-negative integer matrices (contingency tables) with prescribed row and column sums and, more generally, for the number of integer feasible flows in a network. Similarly, we estimate the volume of the polytope of m × n non-negative real matrices with prescribed row and column sums. Our estimates are solutions of convex optimization proble...

An alternating sign matrix is a square matrix with entries 1, 0 and −1 such that the sum of the entries in each row and each column is equal to 1 and the nonzero entries alternate in sign along each row and each column. To some of the symmetry classes of alternating sign matrices and their variations, G. Kuperberg associate square ice models with appropriate boundary conditions, and give determ...

Let ∆1, . . . ,∆K be d × n matrices. We define the row product of these matrices as a d × n matrix, whose rows are entry-wise products of rows of ∆1, . . . ,∆K . This construction arises in certain computer science problems. We study the question, to which extent the spectral and geometric properties of the row product of independent random matrices resemble those properties for a d × n matrix ...

This work deals with the generalized eigenvalue problem for nonsquare matrix pencils A − λB such that matrices A,B ∈ MC (m×n) show a given structure. More precisely, we assume they result from removing the first row of some matrix G ∈ MC ((m+1) , n) in the case of A, and its last row in the case of B. This structured generalized eigenvalue problem can be found in signal processing methods and i...