相关论文: Universal relation between Green's functions in ra…
A universal quantum work relation is proved for isolated time-dependent Hamiltonian systems in a magnetic field as the consequence of microreversibility. This relation involves a functional of an arbitrary observable. The quantum Jarzynski…
We present an alternative procedure to eliminate irregular contributions in the perturbation expansion of c=0-matrix models representing the sum over triangulations of random surfaces, thereby reproducing the results of Tutte [1] and Brezin…
The paper contains two main parts: in the first part, we analyze the general case of $p\geq 2$ matrices coupled in a chain subject to Cauchy interaction. Similarly to the Itzykson-Zuber interaction model, the eigenvalues of the Cauchy chain…
A universality conjecture of Farmer and Rhoades [Trans. Amer. Math. Soc., 357(9):3789--3811, 2005] and Farmer [Adv. Math., 411:Paper No. 108781, 14, 2022] asserts that, under some natural conditions, the roots of an entire function should…
Dependence is undoubtedly a central concept in statistics. Though, it proves difficult to locate in the literature a formal definition which goes beyond the self-evident 'dependence = non-independence'. This absence has allowed the term…
These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the…
Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources. This opens up a new avenue…
A direct relation between the enumeration of ordinary maps and that of fully simple maps first appeared in the work of the first and last authors. The relation is via monotone Hurwitz numbers and was originally proved using Weingarten…
We establish a general map between Grassmann functionals for fermions and probability or weight distributions for Ising spins. The equivalence between the two formulations is based on identical transfer matrices and expectation values of…
Representation theory and the theory of symmetric functions have played a central role in Random Matrix Theory in the computation of quantities such as joint moments of traces and joint moments of characteristic polynomials of matrices…
Eugene Wigner's revolutionary vision predicted that the energy levels of large complex quantum systems exhibit a universal behavior: the statistics of energy gaps depend only on the basic symmetry type of the model. Simplified models of…
We present conditions that allow us to pass from the convergence of probability measures in distribution to the uniform convergence of the associated quantile functions. Under these conditions, one can in particular pass from the asymptotic…
A connection-independent formulation of general relativity is presented, in which the dynamics does not depend on the choice of connection. The gravity action in this formulation includes one additional scalar term in addition to the…
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…
We study two functionals of a random matrix $\boldsymbol A$ with independent elements uniformly distributed over the cyclic group of integers $\{0,1,\ldots, M-1\}$ modulo $M$. One of them, $V_0(\boldsymbol A)$ with mean $\mu$, gives the…
In non-classical linear transport the chord length distribution between collisions is non-exponential and attenuation does not respect Beer's law. Generalized radiative transfer (GRT) extends the classical theory to account for such…
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
Let $A$ be a matrix with nonnegative real entries. A nonnegative factorization of size $k$ is a representation of $A$ as a sum of $k$ nonnegative rank-one matrices. The space of all such factorizations is a bounded semialgebraic set, and we…
We consider Green's functions $G(z):=(H-z)^{-1}$ of Hermitian random band matrices $H$ on the $d$-dimensional lattice $(\mathbb Z/L\mathbb Z)^d$. The entries $h_{xy}=\bar h_{yx}$ of $H$ are independent centered complex Gaussian random…
We generalize the universal power series of Seleznev to several variables and we allow the coefficients to depend on parameters. Then, the approximable functions may depend on the same parameters. The universal approximation holds on…