Journal of Statistical Physics

, Volume 147, Issue 1, pp 35–62 | Cite as

Fluctuation Bounds in the Exponential Bricklayers Process

  • Márton Balázs
  • Júlia Komjáthy
  • Timo Seppäläinen


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.


Interacting particle systems Universal fluctuation bounds t1/3-Scaling Second class particle Convexity Bricklayers process 



M. Balázs and J. Komjáthy were partially supported by the Hungarian Scientific Research Fund (OTKA) grants K100473, K60708, TS49835, F67729, and the Morgan Stanley Mathematical Modeling Center. M. Balázs was also supported by the Bolyai Scholarship of the Hungarian Academy of Sciences. T. Seppäläinen was partially supported by National Science Foundation grants DMS-0701091 and DMS-10-03651, and by the Wisconsin Alumni Research Foundation.


  1. 1.
    Balázs, M.: Microscopic shape of shocks in a domain growth model. J. Stat. Phys. 105(3–4), 511–524 (2001) zbMATHCrossRefGoogle Scholar
  2. 2.
    Balázs, M.: Growth fluctuations in a class of deposition models. Ann. Inst. Henri Poincaré Probab. Stat. 39(4), 639–685 (2003) zbMATHCrossRefGoogle Scholar
  3. 3.
    Balázs, M.: Multiple shocks in bricklayers’ model. J. Stat. Phys. 117, 77–98 (2004) ADSzbMATHCrossRefGoogle Scholar
  4. 4.
    Balázs, M., Farkas, G., Kovács, P., Rákos, A.: Random walk of second class particles in product shock measures. J. Stat. Phys. 139(2), 252–279 (2010) MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. 5.
    Balázs, M., Komjáthy, J., Seppäläinen, T.: Microscopic concavity and fluctuation bounds in a class of deposition processes. Ann. Inst. Henri Poincaré Probab. Stat. 48(1), 151–187 (2012) ADSzbMATHCrossRefGoogle Scholar
  6. 6.
    Balázs, M., Rassoul-Agha, F., Seppäläinen, T., Sethuraman, S.: Existence of the zero range process and a deposition model with superlinear growth rates. Ann. Probab. 35(4), 1201–1249 (2007) MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Balázs, M., Seppäläinen, T.: A convexity property of expectations under exponential weights. (2007)
  8. 8.
    Balázs, M., Seppäläinen, T.: Exact connections between current fluctuations and the second class particle in a class of deposition models. J. Stat. Phys. 127(2), 431–455 (2007) MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. 9.
    Norris, J.R.: Markov Chains. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge (1997) zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Márton Balázs
    • 1
  • Júlia Komjáthy
    • 1
  • Timo Seppäläinen
    • 2
  1. 1.Department of StochasticsBudapest University of Technology and EconomicsBudapestHungary
  2. 2.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA

Personalised recommendations