Related papers: Microscopic universality of complex matrix model c…
The finite-size scaling function of the nonlinear susceptibility of the ferromagnetic Heisenberg chain is given explicitly. It is conjectured that the scaling function is universal for any values of $S$. The conjecture is based on the exact…
We consider random analytic functions defined on the unit disk of the complex plane as power series such that the coefficients are i.i.d., complex valued random variables, with mean zero and unit variance. For the case of complex Gaussian…
In this paper we shall describe some correlation function computations in perturbative heterotic strings that, for example, in certain circumstances can lend themselves to a heterotic generalization of quantum cohomology calculations.…
We consider the asymptotic local behavior of the second correlation function of the characteristic polynomials of sparse non-Hermitian random matrices $X_n$ whose entries have the form $x_{jk}=d_{jk}w_{jk}$ with iid complex standard…
In two-dimensional statistical physics, correlation functions of the O(N) and Potts models may be written as sums over configurations of non-intersecting loops. We define sums associated to a large class of combinatorial maps (also known as…
We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the…
The universal connected correlations proposed recently between eigenvalues of unitary random matrices is examined numerically. We perform an ensemble average by the Monte Carlo sampling. Although density of eigenvalues and a bare…
We consider non-gaussian ensembles of random normal matrices with the constraint that the ensembles are invariant under unitary transformations. We show that the level density of eigenvalues exhibits disk to ring transition in the complex…
We study the two-point correlation functions for the zeroes of systems of $SO(n+1)$-invariant Gaussian random polynomials on $\mathbb{RP}^n$ and systems of ${\rm isom}(\mathbb{R}^n)$-invariant Gaussian analytic functions. Our result…
By universal formulas we understand parameterized analytic expressions that have a fixed complexity, but nevertheless can approximate any continuous function on a compact set. There exist various examples of such formulas, including some in…
{Recently, we found that the correlation between the eigenvalues of random hermitean matrices exhibits universal behavior. Here we study this universal behavior and develop a diagrammatic approach which enables us to extend our previous…
We calculate smoothed correlators for a large random matrix model with a potential containing products of two traces $\tr W_1(M) \cdot \tr W_2(M)$ in addition to a single trace $\tr V(M)$. Connected correlation function of density…
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
Recently a unified hypothesis of multiparameter universality for the critical behavior of bulk and confined anisotropic systems has been formulated [V. Dohm, Phys. Rev. E {\bf 97}, 062128 (2018)]. We prove the validity of this hypothesis on…
The general correlation function for the eigenvalues of $p$ complex hermitian matrices coupled in a chain is given as a single determinant. For this we use a slight generalization of a theorem of Dyson.
Number theorists have studied extensively the connections between the distribution of zeros of the Riemann $\zeta$-function, and of some generalizations, with the statistics of the eigenvalues of large random matrices. It is interesting to…
Recent work on local functional theories of critical inhomogeneous fluids and Ising-like magnets has shown them to be a potentially exact, or near exact, description of universal finite-size effects associated with the excess free-energy…
We introduce a class of fully-connected neural networks whose activation functions, rather than being pointwise, rescale feature vectors by a function depending only on their norm. We call such networks radial neural networks, extending…
Unitary ensembles of large N x N random matrices with a non-Gaussian probability distribution P[H] ~ exp{-TrV[H]} are studied using a theory of polynomials orthogonal with respect to exponential weights. Asymptotically exact expressions for…
We review some recent results concerning the quantitative analysis of the universality classes of two-dimensional statistical models near their critical point. We also discuss the exact calculation of the two--point correlation functions of…