LIMITING CURVES FOR IID RECORDS

We consider the concentration of measure for n i.i.d., two-dimensional random variables under the conditioning that they form a record. Unde r mild conditions, we show that all random variables tend to concentra te, as n --> infinity, around Limiting curves, which are the solutions of an appropriate variational problem. We also show that the same phe nomenon occurs, without the records conditioning, for the longest incr easing subsequence in the sample.