We consider the problem of sampling k-bandlimited graph signals, i.e., linear combinations of the first k graph Fourier modes. We know that a set of k nodes embedding all k-bandlimited signals always exists, thereby enabling their perfect reconstruction after sampling. Unfortunately, to exhibit such a set, one needs to partially diagonalize the graph Laplacian, which becomes prohibitive at larg...

We introduce certain quiver analogue of the determinantal variety. We study the Kempf-Lascoux-Weyman’s complex associated to a line bundle on the variety. In the case of generalized Kronecker quivers, we give a sufficient condition on when the complex resolves a maximal Cohen-Macaulay module supported on the quiver determinantal variety. This allows us to find the set-theoretical defining equat...

We consider a Markov evolution of lozenge tilings of a quarter-plane and study its asymptotics at large times. One of the boundary rays serves as a reflecting wall. We observe frozen and liquid regions, prove convergence of the local correlations to translation-invariant Gibbs measures in the liquid region, and obtain new discrete Jacobi and symmetric Pearcey determinantal point processes near ...

Fischer provided a new type of binomial determinant for the number alternating sign matrices involving third root unity. In this paper we prove that her formula, when replacing unity by an indeterminate q, actually gives (q?1+2+q)-enumeration matrices. By evaluating generalisation are able to reprove conjecture Mills, Robbins and Rumsey stating Q-enumeration is product two polynomials in Q. Fur...

We present several identities involving quasi-minors of noncommutative generic matrices. These identities are specialized to quantum matrices, yielding q-analogues of various classical determinantal formulas.

A determinantal point process (DPP) is a random process useful for modeling the combinatorial problem of subset selection. In particular, DPPs encourage a random subset Y to contain a diverse set of items selected from a base set Y . For example, we might use a DPP to display a set of news headlines that are relevant to a user’s interests while covering a variety of topics. Suppose, however, th...