10 citations · 48 across the 23 of their papers we have counts for
25 papers
Nearest zero-critical point distances for Gaussian SU(2) polynomials
Renjie Feng
We study nearest zero--critical point distances for the Gaussian SU(2) polynomial . For each zero of , let denote its Fubini--Study distance to the neare…
Poisson approximation of the largest gaps between zeros of a stationary Gaussian process
Renjie Feng, Stephen Muirhead
We study the largest gaps between successive zeros of a smooth stationary Gaussian process. Our main result is that, if correlations decay at least polynomially, then after suitabl…
Determinantal point processes on spheres: multivariate linear statistics
Renjie Feng, Friedrich Götze, Dong Yao
In this paper, we will derive the first and 2nd order Wiener chaos decomposition for the multivariate linear statistics of the determinantal point processes associated with the spe…
Zeros of repeated derivatives of random polynomials
Renjie Feng, Dong Yao
It has been shown that zeros of Kac polynomials of degree cluster asymptotically near the unit circle as under some assumptions. This property remains unc…
The Berry-Esseen Theorem for Circular -ensemble
Renjie Feng, Gang Tian, Dongyi Wei
We will prove the Berry-Esseen theorem for the number counting function of the circular -ensemble (CE), which will imply the central limit theorem for the number of points in…
Small gaps of GOE
Renjie Feng, Gang Tian, Dongyi Wei
In this article, we study the smallest gaps of the Gaussian orthogonal ensemble. The main result is that the smallest gaps, after normalized by , will tend to a Poisson distribu…
Large gaps of CUE and GUE
Renjie Feng, Dongyi Wei
In this article, we study the largest gaps of the classical random matrices of CUE and GUE, and show that after rescaling, the limiting densities are given by the Gumbel distributi…
Spectrum of SYK model II: Central limit theorem
Renjie Feng, Gang Tian, Dongyi Wei
In our previous paper \cite{FTD1}, we derived the almost sure convergence of the global density of eigenvalues of random matrices of the SYK model. In this paper, we will prove the…
Spectrum of SYK model III: Large deviations and concentration of measures
Renjie Feng, Gang Tian, Dongyi Wei
In \cite{FTD1}, we proved the almost sure convergence of eigenvalues of the SYK model, which can be viewed as a type of \emph{law of large numbers} in probability theory; in \cite{…
Small gaps of circular -ensemble
Renjie Feng, Dongyi Wei
In this article, we study the smallest gaps of the log-gas -ensemble on the unit circle (CE), where is any positive integer. The main result is that the smallest gaps, af…
Spectrum of SYK model
Renjie Feng, Gang Tian, Dongyi Wei
This is the first part of a series of papers on the spectrum of the SYK model, which is a simple model of the black hole in physics literature. In this paper, we will give a rigoro…
Critical radius and supremum of random spherical harmonics (II)
Renjie Feng, Xingcheng Xu, Robert J. Adler
We continue the study, begun in \cite{FA}, of the critical radius of embeddings, via deterministic spherical harmonics, of fixed dimensional spheres into higher dimensional ones, a…
Critical radius and supremum of random spherical harmonics
Renjie Feng, Robert J. Adler
We first consider {\it deterministic} immersions of the -dimensional sphere into high dimensional Euclidean spaces, where the immersion is via spherical harmonics of level .…
Correlations between zeros and critical points of random analytic functions
Renjie Feng
We study the two-point correlation between zeros and critical points of Gaussian random holomorphic sections over Kähler manifolds. The critical points are point…
Conditional expectations of random holomorphic fields on Riemann surfaces
Renjie Feng
We study two conditional expectations: the expected density of critical points of Gaussian random holomorphic sections of powers of a positive holomorphic line bundle over Riemann…
Critical values of fixed Morse index of random analytic functions on Riemann surfaces
Renjie Feng, Steve Zelditch
This note is an addendum to 'Critical values of random analytic functions on complex manifolds, Indiana Univ. Math. J. 63 No. 3 (2014), 651-686.' by R.Feng and S. Zelditch (arXiv:1…
Median and mean of the Supremum of normalized random holmorphic fields
Renjie Feng, Steve Zelditch
We prove that the expected value and median of the supremum of normalized random holomorphic fields of degree on -dimensional Kähler manifolds are asymptotically of or…
Critical values of random analytic functions on complex manifolds
Renjie Feng, Steve Zelditch
We study the asymptotic distribution of critical values of random holomorphic `polynomials' s_n on a Kaehler manifold M as the degree n tends to infinity. By `polynomial' of degree…
The global existence and convergence of the Calabi flow on
Renjie Feng, Hongnian Huang
In this note, we study the long time existence of the Calabi flow on . Assuming the uniform bound of the total energy, we establish t…
Critical values of Gaussian SU(2) random polynomials
Renjie Feng, Zhenan Wang
In this note, we will get the estimate of the expected distribution of critical values of Gaussian SU(2) random polynomials as the degree large enough. The result is a direct appli…
Random Riesz energies on compact Kähler manifolds
Renjie Feng, Steve Zelditch
This article determines the asymptotics of the expected Riesz s-energy of the zero set of a Gaussian random systems of polynomials of degree N as the degree N tends to infinity in…
Periodic solutions of Abreu's equation
Renjie Feng, Gábor Székelyhidi
We solve Abreu's equation with periodic right hand side, in any dimension. This can be interpreted as prescribing the scalar curvature of a torus invariant metric on an Abelian var…
Large deviations for zeros of random polynomials
Renjie Feng, Steve Zelditch
We extend results of Zeitouni-Zelditch on large deviations principles for zeros of Gaussian random polynomials in one complex variable to certain non-Gaussian ensembles that we…
Bergman metrics and geodesics in the space of Kähler metrics on principally polarized Abelian varieties
Renjie Feng
It's well-known in \kahler geometry that the infinite dimensional symmetric space $\hcal$ of smooth \kahler metrics in a fixed \kahler class on a polarized \kahler manifold is well…