On an Airy matrix model with a logarithmic potential

Kazakov–Migdal Model with Logarithmic Potential and the Double Penner Matrix Model

The Kazakov–Migdal (KM) Model is a U(N) Lattice Gauge Theory with a Scalar Field in the adjoint representation but with no kinetic term for the Gauge Field. This model is formally soluble in the limit N → ∞ though explicit solutions are available for a very limited number of scalar potentials. A “Double Penner” Model in which the potential has two logarithmic singularities provides an example o...

an appropriate model for exchange rate predictability in iran: comparing potential forecastability

nowadays in trade and economic issues, prediction is proposed as the most important branch of science. existence of effective variables, caused various sectors of the economic and business executives to prefer having mechanisms which can be used in their decisions. in recent years, several advances have led to various challenges in the science of forecasting. economical managers in various fi...

An “Airy” Image

Airy Asymptotics: The logarithmic derivative and its reciprocal

We consider the asymptotic expansion of the logarithmic derivative of the Airy function , and also its reciprocal ) ( Ai / ) ( i A z z  ) ( i A / ) ( Ai z z  , as   z . In particular, we derive simple, closed-form solutions for the coefficients which appear in these expansions, of interest since they are encountered in a wide variety of problems. The solutions are presented as Mellin transf...

The Hermitian Two Matrix Model with an Even Quartic Potential

We consider the two matrix model with an even quartic potential W (y) = y/4+αy/2 and an even polynomial potential V (x). The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for the eigenvalues of one of the matrices M1. The vector equilibrium problem is defined for three measures, with external fields on the first and third measures and ...