Related papers: Spectra of sparse non-Hermitian random matrices: a…
We give a deterministic, nearly logarithmic-space algorithm for mild spectral sparsification of undirected graphs. Given a weighted, undirected graph $G$ on $n$ vertices described by a binary string of length $N$, an integer $k\leq \log n$,…
We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on $n$ independent replicates $\left\{X_i(t)\::\: t\in [0,1]\right\}_{1 \leq i \leq n}$, observed…
We propose a novel algorithm for efficiently computing a sparse directed adjacency matrix from a group of time series following a causal graph process. Our solution is scalable for both dense and sparse graphs and automatically selects the…
We present an exclusion process based approach for sampling densest $k$-sub-graphs from regular graphs $L$ with connected complement. By interpreting an exclusion process as a Markov chain on a corresponding Token Graph $\mathfrak{L}_k$, we…
Let (X_{jk})_{j,k>=1} be i.i.d. complex random variables such that |X_{jk}| is in the domain of attraction of an alpha-stable law, with 0< alpha <2. Our main result is a heavy tailed counterpart of Girko's circular law. Namely, under some…
Graph representation matrices are essential tools in graph data analysis. Recently, Hermitian adjacency matrices have been proposed to investigate directed graph structures. Previous studies have demonstrated that these matrices can extract…
The transfer matrix and matrix multiplication ansatz, when applied to nonequilibrium steady states in asymmetric exclusion processed and traffic models, has given many exact results for phase diagrams, bulk densities and fluxes, as well as…
We present a simple strategy to derive universal bounds on the spectral gap of reversible stochastic exchange models on arbitrary graphs. The Kipnis-Marchioro-Presutti (KMP) model, the harmonic process (HP), and the immediate exchange model…
These expository notes are centered around the circular law theorem, which states that the empirical spectral distribution of a nxn random matrix with i.i.d. entries of variance 1/n tends to the uniform law on the unit disc of the complex…
How can we approximate sparse graphs and sequences of sparse graphs (with unbounded average degree)? We consider convergence in the first $k$ moments of the graph spectrum (equivalent to the numbers of closed $k$-walks) appropriately…
We demonstrate that the non-Hermitian quantum geometric tensor (QGT) governs nonlinear electrical responses in systems with a spectral line gap. The quantum metric, which is the symmetric component of the QGT and takes complex values in…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
We consider an ensemble of $2\times 2$ normal matrices with complex entries representing operators in the quantum mechanics of 2 - level parity-time reversal (PT) symmetric systems. The randomness of the ensemble is endowed by obtaining…
A statistical description of part of a many body system often requires a non-Hermitian random matrix ensemble with nature and strength of randomness sensitive to underlying system conditions. For the ensemble to be a good description of the…
We revisit the derivation of the density of states of sparse random matrices. We derive a recursion relation that allows one to compute the spectrum of the matrix of incidence for finite trees that determines completely the low…
We derive exact expressions for the finite-time statistics of extrema (maximum and minimum) of the spatial displacement and the fluctuating entropy flow of biased random walks. Our approach captures key features of extreme events in…
Singular-value statistics (SVS) has been recently presented as a random matrix theory tool able to properly characterize non-Hermitian random matrix ensembles [PRX Quantum {\bf 4}, 040312 (2023)]. Here, we perform a numerical study of the…
In this paper we present a model exhibiting a new type of continuous-time quantum walk (as a quantum mechanical transport process) on networks, which is described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it…
We study the behavior of exponential random graphs in both the sparse and the dense regime. We show that exponential random graphs are approximate mixtures of graphs with independent edges whose probability matrices are critical points of…
Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…