Nonequilibrium fluctuations for a tagged particle in one-dimensional sublinear zero-range processes
Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 3, pp. 611-637.

Nous démontrons les fluctuations hors d'équilibre d'une particule marquée pour une classe de systèmes de particules à portée nulle uni-dimensionels de moyenne nulle dont le taux de sauts croit de manière sous-linéaire. Dans Jara-Landim-Sethuraman (Probab. Theory Related Fields 145 (2009) 565-590), ce résutat a été démontré pour des processus dont le taux croit au moins linéairement. La démonstration du lemme de remplacement dans le cas sous-linéaire exige une nouvelle approche en conséquence des différences entre les propriétés de mélanges des deux processus. La méthode présentée permet également de démontrer les fluctuations d’une particule de deuxième classe dans le modèle à portée nulle symmétrique dont le taux de sauts est égal à 1.

Nonequilibrium fluctuations of a tagged, or distinguished particle in a class of one dimensional mean-zero zero-range systems with sublinear, increasing rates are derived. In Jara-Landim-Sethuraman (Probab. Theory Related Fields 145 (2009) 565-590), processes with at least linear rates are considered. A different approach to establish a main “local replacement” limit is required for sublinear rate systems, given that their mixing properties are much different. The method discussed also allows to capture the fluctuations of a “second-class” particle in unit rate, symmetric zero-range models.

DOI : 10.1214/12-AIHP478
Classification : 60K35
Mots-clés : interacting, particle system, zero-range, tagged, nonequilibrium, diffusion 
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Jara, Milton; Landim, Claudio; Sethuraman, Sunder. Nonequilibrium fluctuations for a tagged particle in one-dimensional sublinear zero-range processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 3, pp. 611-637. doi : 10.1214/12-AIHP478. http://www.numdam.org/articles/10.1214/12-AIHP478/

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