Singular limits of Schrodinger operators and Markov processes

After introducing the Gamma-convergence of a family of symmetric matrices, we study the limits in that sense, of Schrodinger operators on a finite graph. The main result is that any such limit can be interpreted as a Schrodinger operator on a new graph, the construction of which is described explicitly. The operators to which the construction is applied are reversible, almost reducible Markov generators. An explicit method for computing an equivalent of the spectrum is described. Among possible applications, quasi-decomposable processes and low-temperature simulated annealing are studied.