Related papers: Asymptotics of k dimensional spherical integrals a…

We study piecewise polynomial functions $\gamma_k(c)$ that appear in the asymptotics of averages of the divisor sum in short intervals. Specifically, we express these polynomials as the inverse Fourier transform of a Hankel determinant that…

In this {\bf draft version} we prove inhomogeneous Strichartz estimates with spherical symmetry in the abstract setting via duality arguments. Then we derive some new explicit estimates in the context of the wave equation. This allows us to…

We investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state. The limiting distribution was previously investigated via Wishart random matrices indirectly (by…

We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…

We study the behavior of a real $p$-dimensional Wishart random matrix with $n$ degrees of freedom when $n,p\rightarrow\infty$ but $p/n\rightarrow 0$. We establish the existence of phase transitions when $p$ grows at the order…

Many enumeration problems in combinatorics, including such fundamental questions as the number of regular graphs, can be expressed as high-dimensional complex integrals. Motivated by the need for a systematic study of the asymptotic…

Many asymptotic formulas exist for unrestricted integer partitions as well as for distinct partitions of integers into a finite number of parts. Szekeres and Canfield have derived an asymptotic formula for the number of partitions that is…

We consider large non-Hermitian real or complex random matrices $X$ with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of…

Given an $n$-dimensional random vector $X^{(n)}$ , for $k < n$, consider its $k$-dimensional projection $\mathbf{a}_{n,k}X^{(n)}$, where $\mathbf{a}_{n,k}$ is an $n \times k$-dimensional matrix belonging to the Stiefel manifold…

Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…

We calculate a large $k$ asymptotic expansion of the exact surgery formula for Witten's $SU(2)$ invariant of Seifert manifolds. The contributions of all flat connections are identified. An agreement with the 1-loop formula is checked. A…

Sample covariance matrices from multi-population typically exhibit several large spiked eigenvalues, which stem from differences between population means and are crucial for inference on the underlying data structure. This paper…

In this paper we study the asymptotic behavior of the (skew) Macdonald and Jack symmetric polynomials as the number of variables grows to infinity. We characterize their limits in terms of certain variational problems. As an intermediate…

We rewrite Arthur's asymptotic formula for weighted orbital integrals on real groups with the aid of a residue calculus and extend the resulting formula to the Schwartz space. Then we extract the available information about the coefficients…

We compute the quasinormal frequencies of d-dimensional large spherically symmetric black holes with Gauss-Bonnet corrections in the highly damped regime. We solve perturbatively the master differential equation and we compute the…

We introduce the notion of large scale inductive dimension for asymptotic resemblance spaces. We prove that the large scale inductive dimension and the asymptotic dimensiongrad are equal in the class of r-convex metric spaces. This class…

We provide exact asymptotic expressions for the performance of regression by an $L-$layer deep random feature (RF) model, where the input is mapped through multiple random embedding and non-linear activation functions. For this purpose, we…

We determine the asymptotic law for the fluctuations of the total number of critical points of random Gaussian spherical harmonics in the high degree limit. Our results have implications on the sophistication degree of an appropriate…

We consider the Heisenberg spin triangle with general coupling coefficients and general spin quantum number $s$. The corresponding classical system is completely integrable. In the quantum case the eigenvalue problem can be reduced to that…

We show that the spherical integral of the Circular Unitary Ensemble converges in expectation to Euler's generating function for integer partitions, and that subleading corrections to this high-dimensional limit are quasimodular forms.