Related papers: Edge Universality of Beta Ensembles

There is a well-known global equivalence between \Sigma^1_2 sets having the Universal Baire property, two-step \Sigma^1_3 generic absoluteness, and the closure of the universe under the sharp operation. In this note, we determine the exact…

We demonstrate the convergence of the characteristic polynomial of several random matrix ensembles to a limiting universal function, at the microscopic scale. The random matrix ensembles we treat are classical compact groups and the…

We introduce and solve a generalized model of 1+1D Lorentzian triangulations in which a certain subclass of outgrowths is allowed, the occurrence of these being governed by a coupling constant \beta. Combining transfer matrix-, saddle…

It is shown how the universal correlation function of Brezin and Zee, and Beenakker, for random matrix ensembles of Wigner-Dyson type with density support on a finite interval can be derived using a linear response argument and macroscopic…

We introduce iterated beta integrals, a new class of iterated integrals on the universal abelian covering of the punctured projective line that unifies hyperlogarithms and classical beta integrals while preserving their fundamental…

We consider the scalar second order ODE u + |u | $\alpha$ u + |u| $\beta$ u = 0, where $\alpha$, $\beta$ are two positive numbers and the non-linear semi-group S(t) generated on IR 2 by the system in (u, u). We prove that S(t)IR 2 is…

We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the…

Unitarity of the global evolution is an extremely stringent condition on finite state models in discrete spacetime. Quantum cellular automata, in particular, are tightly constrained. In previous work we proved a simple No-go Theorem which…

A spectral set in R^n is a set X of finite Lebesgue measure such that L^2(X) has an orthogonal basis of exponentials. It is conjectured that every spectral set tiles R^n by translations. A set of translations T has a universal spectrum if…

Say a collection of $n$-qu$d$it gates $\Gamma$ is eventually universal if and only if there exists $N_0 \geq n$ such that for all $N \geq N_0$, one can approximate any $N$-qu$d$it unitary to arbitrary precision by a circuit over $\Gamma$.…

We obtain the explicit rate of convergence $N^{-1/2 + \epsilon}$ for the gaps of generalized Wigner matrices in the bulk of the spectrum, for distributions of matrix entries possibly atomic and supported on enough points. The proof proceeds…

For a finite simple graph $G$ we give an upper bound for the regularity of the powers of the edge ideal $I(G)$.

Suppose some classifiers are selected from a set of hypothesis classifiers to form an equally-weighted ensemble that selects a member classifier at random for each input example. Then the ensemble has an error bound consisting of the…

An explicit formula for the mean spectral measure of a random Jacobi matrix is derived. The matrix may be regarded as the limit of Gaussian beta ensemble (G$\beta$E) matrices as the matrix size $N$ tends to infinity with the constraint that…

For general large non-Hermitian random matrices $X$ and deterministic normal deformations $A$, we prove that the local eigenvalue statistics of $A+X$ close to the critical edge points of its spectrum are universal. This concludes the proof…

The eigenvalues for the minors of real symmetric ($\beta=1$) and complex Hermitian ($\beta=2$) Wigner matrices form the Wigner corner process, which is a multilevel interlacing particle system. In this paper, we study the microscopic…

In this paper we prove the universal property of skew $PBW$ extensions generalizing this way the well known universal property of skew polynomial rings. For this, we will show first a result about the existence of this class of…

In the long paper "Family Blowup formula, Admissible Graphs and the Enumeration of Singular Curves (I)" (appearing in JDG), the author solved the enumeration problem of nodal (or general singular) curve counting on algebraic surfaces by…

In this paper, we prove the universality theorem for the iterated integrals of the logarithm of the Riemann zeta-function on some line parallel to the real axis.

We consider a class of particle systems generalizing the $\beta$-Ensembles from random matrix theory. In these new ensembles, particles experience repulsion of power $\beta>0$ when getting close, which is the same as in the…