Condensation and Extremes for a Fluctuating Number of Independent Random Variables

We address the question of condensation and extremes for three classes intimately related stochastic processes: (a) random allocation models zero-range processes, (b) tied-down renewal (c) free processes. While former class number components system is fixed, two other it a fluctuating quantity. Studies these topics are scattered in literature usually dressed up clothing. give stripped-down account subject language sums independent variables order to ourselves consideration particular highlight essentials. Besides giving unified presentation theory, this work investigates facets so far unexplored previous studies. Specifically, we show how study processes can serve as backdrop central present -- then new insights on extreme value statistics which allow deeper understanding mechanism quantitative analysis fluctuations condensate.