Sequences of matrices with increasing size naturally arise in several contexts and especially
in the discretization of continuous problems, such as integral and differential equations. The …

We investigate certain measures induced by families of non-intersecting paths in domino
tilings of the Aztec diamond, rhombus tilings of an abc-hexagon, a dimer model on a …

The analysis of orthogonal polynomials associated with general weights was a major theme
in classical analysis in the twentieth century, and undoubtedly will continue to grow in …

In these lecture notes for the Les Houches School on Applications of Random Matrices in
Physics we give an introduction to the connections between matrix models and topological …

This book describes the theory and applications of discrete orthogonal polynomials--
polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal …

Starting from the finite difference discretization of an elliptic second order PDE as [Formula:
see text] over a bounded domain, we introduce the notion of generalized locally Toeplitz …

This paper concerns the spectral analysis of matrix-sequences that are generated by the
discretization and numerical approximation of partial differential equations, in case the …

The pointwise limit S of a sequence of Stieltjes transforms (Sn) of real Borel probability
measures (Pn) is itself the Stieltjes transform of a Borel pm P if and only if iyS (iy)→− 1 as …

Polynomial ensembles are determinantal point processes associated with (not necessarily
orthogonal) projections onto polynomial subspaces. The aim of this survey article is to put …

We consider the four-vertex model with a special choice of fixed boundary conditions giving
rise to limit shape phenomena. More generally, the considered boundary conditions relate …