Related papers: Correlation functions on the lattice and twisted c…
We evaluate the correlation function of the spectral staircase and use it to evaluate the mesoscopic particle number fluctuations in integrable systems.
Given a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, we develop analytical expressions for the pairwise correlation functions between the layers. These may be calculated…
We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of…
We give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions of independent random variables. Since weighted lattice polynomial functions include…
A flat of a matroid is cyclic if it is a union of circuits. The cyclic flats of a matroid form a lattice under inclusion. We study these lattices and explore matroids from the perspective of cyclic flats. In particular, we show that every…
Polymer models describing the statistics of biomolecules under confinement have applications to a wide range of single molecule experimental techniques and give insight into biologically relevant processes {\em{in vivo}}. In this paper, we…
In this review I discuss intersection numbers of twisted cocycles and their relation to physics. After defining what these intersection number are, I will first discuss a method for computing them. This is followed by three examples where…
A new recursion formula is presented for the correlation functions of the integrable spin 1/2 XXX chain with inhomogeneity. It relates the correlators involving n consecutive lattice sites to those with n-1 and n-2 sites. In a series of…
A review of investigations of running couplings using lattice techniques is given. This includes i) studies of the running of particular non-perturbatively defined renormalized couplings in pure gauge theories over a range of energies, and…
The correlation function of the two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor expansion are…
The correlation functions related to topological phase transitions in inversion-symmetric lattice models described by $2\times 2$ Dirac Hamiltonians are discussed. In one dimension, the correlation function measures the charge-polarization…
The knowledge of the isotropic correlation function of a plane figure is useful to determine the correlation function of the cylinders having the plane figure as right-section and a given height as well as to analyze the out of plane…
The formula for correlation functions based on quantum $A_\infty$ algebras in arXiv:2203.05366, arXiv:2305.11634, and arXiv:2305.13103 requires us to divide the action into the free part and the interaction part. We present a new form of…
We derive a simple analytical expression for the level correlation function of an integrable system. It accounts for both the lack of correlations at smaller energy scales and for global rigidity (level number conservation) at larger…
A method for calculating pair correlation functions in a crystal is developed. The method is based on separating the one- and two- particle correlation functions into the symmetry conserving and the symmetry broken parts. The conserving…
Factorization of string amplitudes is one way of constructing string interaction vertices. We show that correlation functions in string theory can be conveniently factorized using loop variables representing delta functionals. We illustrate…
We compute lattice correlation functions for the model of critical dense polymers on a semi-infinite cylinder of perimeter $n$. In the lattice loop model, contractible loops have a vanishing fugacity whereas non-contractible loops have a…
It is shown that, given a lattice H in a totally disconnected, locally compact group G, the contraction subgroups in G and the values of the scale function on G are determined by their restrictions to H. Group theoretic properties intrinsic…
Starting from an extension of the Poisson bracket structure and Kubo-Martin-Schwinger-property of classical statistical mechanics of continuous systems to spin systems, defined on a lattice, we derive a series of, as we think, new and…
In this note we study the possible connection between functions appearing in diagrammatic expansion and the conformal correlator expansion. To study the connection we propose a generating function which can be expanded to construct a basis.…