Heavy-tailed random variables play an important role in applied
probability and feature prominently in insurance mathematics. The joint
distribution of n independent identically integer-valued distributed
random variables, conditional on the value of the sum, also appears
as the stationary distribution for the zero-range process, a
continuous-time Markov process for interacting particles distributed on
n lattice sites. In this context the transition in large deviations from
Cramer-type collective behavior ("small steps") to big-jump is
interpreted as a transition from gas to condensed phase, and large
deviations for stretched exponential variables act as a toy model for
phase transitions, including a regime of supersaturated gas (a big jump
that does not swallow all of the excess).
The talk presents local large deviations theorems for sums of i.i.d.
\(\mathbb N_0\)-valued, heavy-tailed random variables. The proofs are
inspired by singularity analysis and random combinatorial structures.
Based on joint work with N. M. Ercolani and D. Ueltschi (J. Theoret.
Probab., 2018).
Angelegt am Monday, 03.09.2018 11:23 von Anita Kollwitz
Geändert am Monday, 07.01.2019 10:06 von Anita Kollwitz
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