LARGEST EIGENVALUE DISTRIBUTION IN THE DOUBLE SCALING LIMIT OF MATRIXMODELS - A COULOMB FLUID APPROACH

Using thermodynamic arguments we find that the probability that there are no eigenvaIues in the interval (-s, infinity) in the double scalin g limit of Hermitian matrix models is O(exp(-s(2 gamma)+2)) as s --> infinity. Here gamma = m - 1/2, m = 1,2,... determines the mth multicr itical point of the level density: sigma(x) proportional to b[1 - (x/b )(2)](gamma), x is an element of (-b, b) and b(2) proportional to N. F urthermore, the size of the transition zone, where the eigenvalue dens ity becomes vanishingly small at the tail of the spectrum, is approxim ate to N((gamma-1))/2((gamma+1)) in agreement with earlier work based upon the string equation.