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 no...

Given a representation of compact Lie group and state we define probability measure on the coadjoint orbits dominant weights by considering decomposition into irreducible components. For large tensor powers independent copies show that induced distributions converge to value moment map. faithful states prove measures satisfy deviation principle with an explicitly given rate function.