I review some of the things we have learned about large N gauge theories (and QCD ∞) from lattice calculations in recent years. I point to some open problems.

A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...

This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...

One concern in using photonic band-gap fiber (PBGF) as a gas sensor is the response time. In this type of the gas sensors, response time is the time required for gas to diffuse into the hollow-core. So considering a large hollow-core PBGF (HC-PBGF), the response time can be significantly reduced. But in the large HC-PBGF, the fundamental issue is the presence of higher order modes (HOMs). Somet...

Many hierarchical techniques to solve large Markov decision processes (MDPs) are based on the partition of the state space into strongly connected components (SCCs) that can be classified into some levels. In each level, smaller problems named restricted MDPs are solved, and then these partial solutions are combined to obtain the global solution. In this paper, we first propose a novel algorith...