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Constraint-driven condensation in large fluctuations of linear statistics
Juraj Szavits-Nossan1, Martin R Evans1, Satya N Majumdar2
1SUPA, School of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom.
Physical Review Letters
|February 4, 2014
Summary
Condensation, a key aggregation phenomenon, can occur in systems with lighter probability distributions than previously thought. This study reveals how constraints enable condensation, even with less heavy-tailed distributions.
Area of Science:
- Probability Theory
- Statistical Mechanics
- Complex Systems
Background:
- Condensation describes how a single random variable dominates a sum.
- This phenomenon is observed in physical systems like granular media and traffic jams.
- Typically, condensation requires probability distributions with heavy tails (heavier than exponential).
Purpose of the Study:
- To investigate condensation in probability distributions with lighter tails than exponential.
- To explore the role of additional constraints in inducing condensation.
- To analyze the behavior of sample variance under specific conditions.
Main Methods:
- Mathematical modeling of condensation phenomena.
- Analysis of probability distributions conditioned on sample mean values.
- Investigation of phase transitions in statistical systems.
- Examination of large deviation rate functions.
Main Results:
- Demonstrated that condensation can occur with light-tailed distributions when constraints are present.
- Identified a phase transition in the probability distribution of sample variance, conditioned on the sample mean.
- Observed a change in the large deviation rate function at this transition point.
Conclusions:
- The study extends the understanding of condensation beyond heavy-tailed distributions.
- Constraints can fundamentally alter aggregation dynamics in random variable sums.
- The findings have implications for diverse physical systems exhibiting condensation.
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