abstract: In the last decade, a new universal law called the Tracy-Widom distribution has emerged, which describes the typical fluctuations of the extremum in several strongly interacting systems. But how sensitive is this universality against the pair interactions ? In this talk, I will address this question in the context of extreme statistics in a many-body system interacting via the one dimensional linear Coulomb repulsive potential. We found that the extreme statistics in this system is different from that described by the Tracy-Widom distribution however, the large deviation functions still predict a third order transition. At the end, I will briefly discuss about the index and the gap distributions in this system.