Related papers: Joint spectrum and large deviation principle for r…

We study asymptotics of random shifted Young diagrams which correspond to a given sequence of reducible projective representations of the symmetric groups. We show limit results (Law of Large Numbers and Central Limit Theorem) for their…

We consider the probability of having two intervals (gaps) without eigenvalues in the bulk scaling limit of the Gaussian Unitary Ensemble of random matrices. We describe uniform asymptotics for the transition between a single large gap and…

The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…

Suppose that A_1,\dots, A_N are independent random matrices whose atoms are iid copies of a random variable \xi of mean zero and variance one. It is known from the works of Newman et. al. in the late 80s that when \xi is gaussian then…

We study (asymmetric) $U$-statistics based on a stationary sequence of $m$-dependent variables; moreover, we consider constrained $U$-statistics, where the defining multiple sum only includes terms satisfying some restrictions on the gaps…

We establish a large deviation principle (LDP) for probability graphons, which are symmetric functions from the unit square into the space of probability measures. This notion extends classical graphons and provides a flexible framework for…

In this paper, a connection between bi-free probability and the asymptotics of random quantum channels and tensor products of random matrices is established. Using bi-free matrix models, it is demonstrated that the spectral distribution of…

We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (1975) has shown that the long term behaviour of this process has a phase transition: If the particle production…

We establish some conditions under which $\text{GL}(d,\mathbb{R})$-valued cocycles over a subshift of finite type, equipped with an equilibrium state, exhibit exponential asymptotics for the spectral radius. Specifically, we show that the…

This paper is a survey article on the limiting behavior of the discrete spectrum of the right regular representation in $L^2(\Gamma\bs G)$ for a lattice $\Gamma$ in a reductive group $G$ over a number field. We discuss various aspects of…

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{FTD2}, we proved that the linear statistic of eigenvalues…

We study largest singular values of large random matrices, each with mean of a fixed rank $K$. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It…

In Random Matrix Theory the local correlations of the Laguerre and Jacobi Unitary Ensemble in the hard edge scaling limit can be described in terms of the Bessel kernel (containing a parameter $\alpha$). In particular, the so-called hard…

For products $P_N$ of $N$ random matrices of size $d \times d$, there is a natural notion of finite $N$ Lyapunov exponents $\{\mu_i\}_{i=1}^d$. In the case of standard Gaussian random matrices with real, complex or real quaternion elements,…

Let $G=\mathop{A\ast B}\limits_C$ be an amalgamated product of finite rank free groups $A$, $B$ and $C$. We introduce atomic measures and corresponding asymptotic densities on a set of normal forms of elements in $G$. We also define two…

We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem (LCLT) for non-autonomous dynamical systems. A key advance is the extension of the spectral…

In this article, we consider limit theorems for some weighted type random sums (or discrete rough integrals). We introduce a general transfer principle from limit theorems for unweighted sums to limit theorems for weighted sums via rough…

In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…

Several important families of computational and statistical results in machine learning and randomized algorithms rely on uniform bounds on quadratic forms of random vectors or matrices. Such results include the Johnson-Lindenstrauss (J-L)…

Asymptotics deviation probabilities of the sum S n = X 1 + $\times$ $\times$ $\times$ + X n of independent and identically distributed real-valued random variables have been extensively investigated, in particular when X 1 is not…