On likely solutions of the stable matching problem with unequal numbers of men and women

Following up a recent work by Ashlagi, Kanoria and Leshno, we study a stable matching problem with unequal numbers of men and women, and independent uniform preferences. The asymptotic formulas for the expected number of stable matchings, and for the probabilities of one point--concentration for the range of husbands' total ranks and for the range of wives' total ranks are obtained.