Precise Large Deviations for Sums of Dependent Variables

Speakers: Thomas Lehéricy\n\nLarge deviations theory deals with the convergence of the logarithm of the probability of a rare event. Precise large deviations, on the other hand, provides an asymptotic equivalent for the probability of such an event itself, rather than for its logarithm. Results of this kind have been available for sums of i.i.d. random variables since the work of Bahadur and Rao (1960). Establishing such bounds becomes significantly more challenging once the i.i.d. assumption is dropped. I will present joint work with Ashkan Nikeghbali, Pierre-Loïc Méliot, and Mariia Khodiakova on this problem, with applications to the classical question of counting triangles in the Erdős–Rényi random graph, as well as to other combinatorial models.\n\nhttps://indico.math.cnrs.fr/event/16526/