Related papers: Supereigenvalue Models and Topological Recursion
We develop the systematics for applying operators on Minkowski correlation functions to get the inflationary correlation functions. Simple structures and recursion relations are known for Minkowski correlation functions. Using the operator…
The evaluation homomorphisms from the super Yangian $\Ymn$ to the universal enveloping algebra $\U(\gl_{m|n})$ allows one to regard the covariant tensor module of $\gl_{m|n}$ as $\Ymn$ modules. We study simple quotients of the submodules…
We calculate three- and four-point functions in super Liouville theory coupled to super Coulomb gas on world sheets with spherical topology. We first integrate over the zero mode and assume that a parameter takes an integer value. After…
In the spirit of the Head-Gordon-Pople algorithm, we report vertical, transfer and horizontal recurrence relations for the efficient and accurate computation of four-electron integrals over Gaussian basis functions. Our recursive approach…
It is shown how to obtain superconformal Toda models as reductions of WZNW theories based on any Lie or super--Lie algebra.
In this paper we prove, in a purely combinatorial way, a structural quasi-polynomiality property for the Bousquet-M\'elou-Schaeffer numbers. Conjecturally, this property should follow from the Chekhov-Eynard-Orantin topological recursion…
In this note we compute the functional derivative of the induced charge density, on a thin conductor, consisting of the union of g+1 disjoint intervals, $J:=\cup_{j=1}^{g+1}(a_j,b_j),$ with respect to an external potential. In the context…
It is well known that Feynman integrals in dimensional regularization often evaluate to functions of hypergeometric type. Inspired by a recent proposal for a coaction on one-loop Feynman integrals in dimensional regularization, we use…
This paper presents the Gaussian subordination framework to generate optimal one-sided approximations to multidimensional real-valued functions by functions of prescribed exponential type. Such extremal problems date back to the works of…
New recursion relations for the Riemann zeta function are introduced. Their derivation started from the standard functional equation. The new functional equations have both real and imaginary increment versions and can be applied over the…
An algorithm is given for computing explicit formulas for the generators of relations among the invariant rational functions for vector-valued bilinear forms. These formulas have applications in the geometry of Riemannian submanifolds and…
We give simple linear algebraic proofs of Eynard-Mehta theorem, Okounkov-Reshetikhin formula for the correlation kernel of the Schur process, and Pfaffian analogs of these results. We also discuss certain general properties of the spaces of…
K. Saito's theory of primitive forms gives a natural semi-simple Frobenius manifold structure on the space of miniversal deformations of an isolated singularity. On the other hand, Givental introduced the notion of a total ancestor…
We adopt the viewpoint that topological And\'e-Quillen theory for commutative $S$-algebras should provide usable (co)homology theories for doing calculations in the sense traditional within Algebraic Topology. Our main emphasis is on…
Data sets collected at different times and different observing points can possess correlations at different times $and$ at different positions. The doubly correlated Wishart model takes both into account. We calculate the eigenvalue density…
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…
We give direct and inverse theorems for the weighted approximation of functions with endpoint singularities by combinations of Bernstein operators.
We give a constructive proof for the superbosonization formula for invariant random matrix ensembles, which is the supersymmetry analog of the theory of Wishart matrices. Formulas are given for unitary, orthogonal and symplectic symmetry,…
We consider the problem of recovering a unitary eigendecomposition of a complex unitary matrix from that of its embedded real-valued formulation. Such formulations arise naturally in scientific computing workflows that employ…
We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with the algorithmic theory of contiguous relations, which…