Conditional Distribution of Heavy Tailed Random Variables on Large Deviations of their Sum

Abstract

It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are distributed when a large deviation of their sum is observed.

Results on local conditioning added

References in corpus (4)

• Large deviations for random walks under subexponentiality: the big-jump domain
• Zero Range Condensation at Criticality
• Condensation for a fixed number of independent random variables
• Asymptotics for sums of random variables with local subexponential behaviour

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• Condensation for random variables conditioned by the value of their sum
• Condensation and extremes for a fluctuating number of independent random variables
• Structure of the condensed phase in the inclusion process
• Conditioned random walks and interaction-driven condensation
• Monotonicity and Condensation in Homogeneous Stochastic Particle Systems
• Large fluctuations and transport properties of the Lévy-Lorentz gas
• Metastable Markov chains
• Metastable behavior of weakly mixing Markov chains: the case of reversible, critical zero-range processes
• Large deviation Local Limit Theorems and limits of biconditioned Trees and Maps
• Localization, big-jump regime and the effect disorder for a class of generalized pinning models
• Condensation in models with factorized and pair-factorized stationary states
• Emergence of interlacements from the finite volume Bose soup
• Stretched random walks and the behaviour of their summands
• Quantitative bounds for large deviations of heavy tailed random variables
• Critical Fluctuations in Renewal Models of Statistical Mechanics
• Condensation transition in a conserved generalized interacting zero-range process
• Parking on Cayley trees & Frozen Erdös-Rényi
• Probabilities of large values for sums of i.i.d. non-negative random variables with regular tail of index $-1$
• A note on limiting behaviour of constrained sums of two variables