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.
On the asymptotic behaviour of random recursive trees in random environment
Asymptotic behaviour of exponential functionals of Lévy processes with applications to random processes in random environment
Asymptotic behaviour of the one-dimensional "rock-paper-scissors" cyclic cellular automaton
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