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 disorder operators in a free theory of complex bosonic and fermionic field, correlators ruled by a Painlevè differential equation.

Our interest is in the scaled joint distribution associated with k-increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifying in terms of correlation functions the same distribution for a Poissonized model in which both the number of symbols in the involution, and the number of fixed points, are random variables. From this, a de-Poissonizat...

We study the problem of computing correlation between two piecewise-linear bivariate functions defined over a common domain, where the surfaces they define in three dimensions— polyhedral terrains—can be transformed vertically by a linear transformation of the third coordinate (scaling and translation). We present a randomized algorithm that minimizes the maximum vertical distance between the g...

Combining the stochastic and δN formalisms, we derive non-perturbative analytical expressions for all correlation functions of scalar perturbations in single-field, slow-roll inflation. The standard, classical formulas are recovered as saddle-point limits of the full results. This yields a classicality criterion that shows that stochastic effects are small only if the potential is sub-Planckian...

The ability to measure characteristics of source shapes using nonidentical particle correlations is discussed. Both strong-interaction induced and Coulomb induced correlations are shown to provide sensitivity to source shapes. By decomposing correlation functions with spherical or Cartesian harmonics, details of the shapes can be especially well isolated.

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 work to the case in which the random matrix evolves in time or varies as some external parameters vary. We compute the current-current correlation function, disc...

This paper considers the cross-correlation function values of a family of binary sequences obtained born finite geometries. These values are shown to depend on the intersection of hyperplanes in a projective space and the cross-correlation function values of the nonlinear feedforward functions used in the construction of the geometric sequences.

Cluster expansions were introduced at the dawn of Statistical Mechanics for the study of high temperature gases of interacting particles. They constitute a powerful perturbative method that is suitable for geometrically large systems, such as encountered in Statistical Physics. Numerous articles have contributed to the subject; a list of relevant publications is [GK, Cam, Bry, KP, Pfi, Dob, BZ,...

We are ultimately interested in developing a set of expressions that describe a system at all times and frequencies. In section 2, we will introduce the projection operator and use it to derive the Generalized Langevin Equation. The projection operator allows us to study only the portion of the system we are interested in, and treat the rest as a statistical bath. In section 3, we will use the ...

Four-dimensional N -extended superconformal symmetry and correlation functions of quasi-primary superfields are studied within the superspace formalism. A superconformal Killing equation is derived and its solutions are classified in terms of supertranslations, dilations, Lorentz transformations, R-symmetry transformations and special superconformal transformations. In general, due to the invar...