The PCP theorem states that NP PCP(log n; (log n) c). We build gradually towards its proof. As an intermediate step we show that NP PCP(log n; (log n) c) for some constant c > 1. The presentation here is taken in most parts from 4] (which is heavily based on 2], where NP PCP(log n log log n; log n log log n) was proved. We save a log log n factor in the number of random bits (at a cost of a pol...

A central limit theorem for stochastic recursive sequences of topical operators. Abstract Let (A n) n∈N be a stationary sequence of topical (i.e. isotone and ad-ditively homogeneous) operators. Let x(n, x 0) be defined by x(0, x 0) = x 0 and x(n + 1, x 0) = A n x(n, x 0). It can modelize a wide range of systems including train or queuing networks, job-shop, timed digital circuits or parallel pr...