AbstractStarting from the symmetric reduction of Cauchy bi-orthogonal polynomials, we derive the Toda equation of CKP type (or the C-Toda lattice) as well as its Lax pair by introducing the time flow. Determinant solutions of the C-Toda lattice are expressed in terms of matrix integrals which can be extended to give matrix integral solutions of the CKP hierarchy. It is remarkable that the time-...
AbstractKinetic Brownian motion is a stochastic process that interpolates between the geodesic flow and Laplacian. It is also an analogue of Bismut’s hypoelliptic Laplacian. We prove the strong convergence of the spectrum of kinetic Brownian motion to the spectrum of base Laplacian for all compact Riemannian manifolds. This generalizes recent work of Kolb--Weich--Wolf on constant curvature sur...