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We define the determinantal divisor rank of an integral matrix to be the number of invariant factors which equal 1. Some properties of the determinantal divisor rank are proved, which are analogous to known properties of the usual rank. These include the Frobenious inequality for the rank of a product and a relation between the rank of a submatrix of a matrix and that of its complementary subma...

The Papangelou intensities of determinantal (or fermion) point processes are investigated. These exhibit a monotonicity property expressing the repulsive nature of the interaction, and satisfy a bound implying stochastic domination by a Poisson point process. We also show that determinantal point processes satisfy the so-called condition ( λ), which is a general form of Gibbsianness. Under a co...

We propose periodic Macdonald processes as a $(q,t)$-deformation of Schur and analogue processes. It is known that, in the theory stochastic related to family symmetric functions, Cauchy-like identity gives an explicit expression partition function. compute functions relying on free field realization theory. also study several families observables for give formulas their moments. The technical ...

We present a novel probabilistic model for distributions over sets of structures— for example, sets of sequences, trees, or graphs. The critical characteristic of our model is a preference for diversity: sets containing dissimilar structures are more likely. Our model is a marriage of structured probabilistic models, like Markov random fields and context free grammars, with determinantal point ...