FROM RANDOM-WALKS TO SPIN-GLASSES

The talk was a short review on systems which exhibit non-self-averagin g effects: sums of random variables when the distribution has a long t ail, mean field spin glasses, random map models and returns of a rando m walk to the origin, Non-self-averaging effects are identical in the case of sums of random Variables and in the spin glass problem as pred icted by the replica approach. Also we will see that for the random ma p models or for the problem of the returns of a random walk to the ori gin, the non-self-averaging effects coincide with the results of the r eplica approach when the number n of replica n = -1/2 or n = -1.