13 - 17 • San Jose, CA • AIM SQuaRE

]]>In the spirit of the theory of Schur processes, we define probability measures on sequences of signatures with probability weights proportional to products of our symmetric functions. We show that these measures can be viewed as determinantal point processes, and we express their correlation kernels in a double contour integral form. We present two proofs: The first is a direct computation of Eynard–Mehta type, and the second uses non-standard, inhomogeneous versions of fermionic operators in a Fock space coming from the algebraic Bethe Ansatz for the six vertex model.

We also interpret our determinantal processes as random domino tilings of a half-strip with inhomogeneous domino weights. In the bulk, we show that the lattice asymptotic behavior of such domino tilings is described by a new determinantal point process on $\mathbb{Z}^{2}$, which can be viewed as an doubly-inhomogeneous generalization of the extended discrete sine process.

]]>4/18 – 6/3 (a week in this range) • Florence, Italy • Program “Randomness, Integrability and Universality” at Galileo Galilei Institute

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