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2021 | OriginalPaper | Buchkapitel

Central Limit Theorems for a Driven Particle in a Random Medium with Mass Aggregation

verfasst von : Luiz Renato Fontes, Pablo Almeida Gomes, Rémy Sanchis

Erschienen in: In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius

Verlag: Springer International Publishing

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Abstract

We establish central limit theorems for the position and velocity of the charged particle in the mechanical particle model introduced by Fontes, Jordão Neves and Sidoravicius (2000).

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Fußnoten
1
The distinction of the initial mass of the t.p. with respect to the other particles, absent in [4], is for convenience only; any positive initial mass for the t.p. would not change our results, but values 1 or below would require unimportant complications in our arguments.
 
Literatur
1.
Zurück zum Zitat Boldrighini, C., Pellegrinotti, A., Presutti, E., Sinai, Ya., Soloveitchik, M.: Ergodic properties of a semi-infinite one-dimensional system of statistical mechanics. Comm. Math. Phys. 101, 363–382 (1985) Boldrighini, C., Pellegrinotti, A., Presutti, E., Sinai, Ya., Soloveitchik, M.: Ergodic properties of a semi-infinite one-dimensional system of statistical mechanics. Comm. Math. Phys. 101, 363–382 (1985)
2.
Zurück zum Zitat Buttà, P., Caglioti, E., Marchioro, C.: On the violation of Ohm’s law for bounded interactions: a one dimensional system. Comm. Math. Phys. 249, 353–382 (2004)MathSciNetCrossRef Buttà, P., Caglioti, E., Marchioro, C.: On the violation of Ohm’s law for bounded interactions: a one dimensional system. Comm. Math. Phys. 249, 353–382 (2004)MathSciNetCrossRef
3.
Zurück zum Zitat De La Peña, V.H., Giné, E.: Decoupling: From Dependence to Independence. Probability and Its Applications. Springer, Berlin (1999) De La Peña, V.H., Giné, E.: Decoupling: From Dependence to Independence. Probability and Its Applications. Springer, Berlin (1999)
4.
Zurück zum Zitat Fontes, L.R.G., Jordão Neves, E., Sidoravicius, V.: Limit velocity for a driven particle in a random medium with mass aggregation. Ann. Inst. H. Poincaré Probab. Statist. 36, 787–805 (2000)MathSciNetCrossRef Fontes, L.R.G., Jordão Neves, E., Sidoravicius, V.: Limit velocity for a driven particle in a random medium with mass aggregation. Ann. Inst. H. Poincaré Probab. Statist. 36, 787–805 (2000)MathSciNetCrossRef
5.
Zurück zum Zitat Lifshits, M., Shi, Z.: Aggregation rates in one-dimensional stochastic systems with adhesion and gravitation. Ann. Probab. 33, 53–81 (2005)MathSciNetCrossRef Lifshits, M., Shi, Z.: Aggregation rates in one-dimensional stochastic systems with adhesion and gravitation. Ann. Probab. 33, 53–81 (2005)MathSciNetCrossRef
6.
Zurück zum Zitat Martin, Ph.A., Piasecki, J.: Aggregation dynamics in a self-gravitating one-dimensional gas. J. Statist. Phys. 84, 837–857 (1996)MathSciNetCrossRef Martin, Ph.A., Piasecki, J.: Aggregation dynamics in a self-gravitating one-dimensional gas. J. Statist. Phys. 84, 837–857 (1996)MathSciNetCrossRef
7.
Zurück zum Zitat Pellegrinotti, A., Sidoravicius, V., Vares, M.E.: Stationary state and diffusion for a charged particle in a one-dimensional medium with lifetimes. Teor. Veroyatnost. i Primenen. 44, 796–825 (2000); Reprinted in Theory Probab. Appl. 44, 697–721 (1999) Pellegrinotti, A., Sidoravicius, V., Vares, M.E.: Stationary state and diffusion for a charged particle in a one-dimensional medium with lifetimes. Teor. Veroyatnost. i Primenen. 44, 796–825 (2000); Reprinted in Theory Probab. Appl. 44, 697–721 (1999)
8.
Zurück zum Zitat Sidoravicius, V., Triolo, L., Vares, M.E.: On the forced motion of a heavy particle in a random medium. I. Existence of dynamics. I Brazilian School in Probability (Rio de Janeiro, 1997). Markov Process. Relat. Fields 4, 629–647 (1998)MATH Sidoravicius, V., Triolo, L., Vares, M.E.: On the forced motion of a heavy particle in a random medium. I. Existence of dynamics. I Brazilian School in Probability (Rio de Janeiro, 1997). Markov Process. Relat. Fields 4, 629–647 (1998)MATH
9.
Zurück zum Zitat Sidoravicius, V., Triolo, L., Vares, M.E.: Mixing properties for mechanical motion of a charged particle in a random medium. Comm. Math. Phys. 219, 323–355 (2001)MathSciNetCrossRef Sidoravicius, V., Triolo, L., Vares, M.E.: Mixing properties for mechanical motion of a charged particle in a random medium. Comm. Math. Phys. 219, 323–355 (2001)MathSciNetCrossRef
Metadaten
Titel
Central Limit Theorems for a Driven Particle in a Random Medium with Mass Aggregation
verfasst von
Luiz Renato Fontes
Pablo Almeida Gomes
Rémy Sanchis
Copyright-Jahr
2021
DOI
https://doi.org/10.1007/978-3-030-60754-8_18