A bstract We propose a useful integral representation of the quenched free energy which is applicable to any random systems. Our formula involves generating function multi-boundary correlators, can be interpreted on bulk gravity side as spacetime D-branes introduced by Marolf and Maxfield in [arXiv:2002.08950]. As an example, we apply our formalism Airy limit matrix model compute its under cert...

We consider an analogue of Kontsevich's matrix Airy function where the cubic potential $\mathrm{Tr}(\Phi^3)$ is replaced by a quartic term $\mathrm{Tr}(\Phi^4)$. Cumulants resulting measure are known to decompose into cycle types for which recursive system equations can be established. develop new, purely algebraic geometrical solution strategy two initial recursion, based on properties Cauchy ...

A formalism is developed to obtain the energy eigenvalues of spatially confined quantum mechanical systems in the framework of the usual Wentzel-Kramers-Brillouin (WKB) and Modified Airy Function (MAF) methods. To illustrate the working rule, the techniques are applied to 3 different cases, viz. the confined 1-dimensional harmonic and quartic oscillators, and a boxed-in charged particle subject...

Gaussian and Chiral β-Ensembles, which generalise well known orthogonal (β = 1), unitary (β = 2), and symplectic (β = 4) ensembles of random Hermitian matrices, are considered. Averages are shown to satisfy duality relations like {β,N, n} ⇔ {4/β, n,N} for all β > 0, where N and n respectively denote the number of eigenvalues and products of characteristic polynomials. At the edge of the spectru...

We present a numerical study of the giant Goos-Hänchen shifts (GHSs) obtained from an Airy beam impinging on a nonlinear interface. To avoid any angular restriction associated with the paraxial approximation, the analysis is based on the nonlinear Helmholtz equation. We report the existence of nonstandard nonlinear GHSs displaying an extreme sensitivity to the input intensity and the existence ...

In this paper we consider the stochastic six-vertex model in quadrant started with step initial data. After a long time T, it is known that one-point height function fluctuations are of order $$T^{1/3}$$ and governed by Tracy–Widom distribution. We prove two-point distribution function, rescaled horizontally $$T^{2/3}$$ vertically , converges to Airy process. The starting point result recent co...