Asymptotics of a Class of Operator Determinants
  In previous work of C. A. Tracy and the author asymptotic formulas were derived for certain operator determinants whose interest lay in the fact that quotients of them gave solutions to the cylindrical Toda equations. In the present paper we consider a more general class of operators which retain some of the properties of those cited and we find analogous asymptotics for the determinants 
Harold Widom