Fluctuation Bounds in the Exponential Bricklayers Process

Márton Balázs*, Júlia Komjáthy, Timo Seppäläinen

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review


This paper is the continuation of our earlier paper (Balázs et al. in Ann. Inst. Henri Poincaré Probab. Stat. 48(1):151-187, 2012), where we proved t 1/3-order of current fluctuations across the characteristics in a class of one dimensional interacting systems with one conserved quantity. We also claimed two models with concave hydrodynamic flux which satisfied the assumptions which made our proof work. In the present note we show that the totally asymmetric exponential bricklayers process also satisfies these assumptions. Hence this is the first example with convex hydrodynamics of a model with t 1/3-order current fluctuations across the characteristics. As such, it further supports the idea of universality regarding this scaling.

Original languageEnglish
Pages (from-to)35-62
Number of pages28
JournalJournal of Statistical Physics
Issue number1
Publication statusPublished - Apr 2012


  • Bricklayers process
  • Convexity
  • Interacting particle systems
  • Second class particle
  • t -Scaling
  • Universal fluctuation bounds

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