  Using thermodynamic arguments we find that the probability that there are no
eigenvalues in the interval (-s,\infty) in the double scaling limit of
Hermitean matrix models is O(exp(-s^{2m+1})) as s\to+\infty.Here m=1,2,3..
determine the m^{th} multi-critical point of the level density:\sigma(x)\sim
b[1-(x/b)^2]^{m-1/2} and b^2\sim N.Furthermore,the size of the transition zone
where the eigenvalue density becomes vanishingly small at the tail of the
spectrum is \sim N^{(m-3/2)/(2m+1)} in agreement with earlier work based on the
string equation.
