RECORDS IN GEOMETRICALLY DISTRIBUTED WORDS: SUM OF POSITIONS

Kortchemski introduced a new parameter for random permutations: thesum of the positions of the records. We investigate this parameter in the context of random words, where the letters are obtained by geometric probabilities. We find a relation for a bivariate generating function, from which we can obtain the expectation, exactly and asymptotically. In principle, one could get all moments from it, but the computations would be huge.