# On large deviations for combinatorial sums

## TL;DR

This paper studies the asymptotic probabilities of large deviations in normalized combinatorial sums, identifying conditions under which these probabilities align with the standard normal tail, extending classical results.

## Contribution

It introduces new conditions for large deviation asymptotics of combinatorial sums, expanding the understanding of their convergence to normal distribution tails.

## Key findings

- Probabilities of large deviations match the standard normal tail in a specific zone.
- Conditions similar to Bernstein's condition are sufficient for normal approximation.
- The zone of normal convergence can grow at a power rate.

## Abstract

We investigate asymptotic behaviour of probabilities of large deviations for normalized combinatorial sums. We find a zone in which these probabilities are equivalent to the tail of the standard normal law. Our conditions are similar to the classical Bernstein condition. The range of the zone of the normal convergence can be of power order.