Motivated by two former conjectures “Tomaszewski’s conjecture and Hitczenko-Kwapień’s conjecture”, in this paper, we study concentration property and anti-concentration property of the Student’s -distribution. Concretely, we study the infimum values of two probability functions for the Student’s -distribution with respective to the degrees of freedom. We thank one associate editor and two referees for very helpful suggestions and comments that helped improving the presentation of the paper.
