Electronic Communications in Probability

One dimensional annihilating and coalescing particle systems as extended Pfaffian point processes

Roger Tribe, Jonathan Yip, and Oleg Zaboronski

Full-text: Open access

Abstract

We prove that the multi-time particle distributions for annihilating or coalescing Brownian motions, under the maximal entrance law on the real line, are extended Pfaffian point processes. <strong>There is an erratum in</strong> <a href="http://dx.doi.org/10.1214/ECP.v20-4302"><strong>ECP volume 20 paper 46</strong></a>.<br /><br />

Article information

Source
Electron. Commun. Probab., Volume 17 (2012), paper no. 40, 7 pp.

Dates
Accepted: 6 September 2012
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465263173

Digital Object Identifier
doi:10.1214/ECP.v17-2133

Mathematical Reviews number (MathSciNet)
MR2981896

Zentralblatt MATH identifier
1252.60095

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60G55: Point processes

Keywords
Extended Pfaffian point process annihilating Brownian motions coalescing Brownian motions

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Tribe, Roger; Yip, Jonathan; Zaboronski, Oleg. One dimensional annihilating and coalescing particle systems as extended Pfaffian point processes. Electron. Commun. Probab. 17 (2012), paper no. 40, 7 pp. doi:10.1214/ECP.v17-2133. https://projecteuclid.org/euclid.ecp/1465263173


Export citation

References

  • Anderson, Greg W.; Guionnet, Alice; Zeitouni, Ofer. An introduction to random matrices. Cambridge Studies in Advanced Mathematics, 118. Cambridge University Press, Cambridge, 2010. xiv+492 pp. ISBN: 978-0-521-19452-5
  • Arratia, Richard. Limiting point processes for rescalings of coalescing and annihilating random walks on ${\bf Z}^{d}$. Ann. Probab. 9 (1981), no. 6, 909–936.
  • ben-Avraham, Daniel; Brunet, Éric. On the relation between one-species diffusion-limited coalescence and annihilation in one dimension. J. Phys. A 38 (2005), no. 15, 3247–3252.
  • ben Avraham, D.: Complete Exact Solution of Diffusion-Limited Coalescence, A+A -> A. phPhys. Rev. Lett. 81, (1988), 4756. ben Avraham, D. and Masser, T.: Correlation functions for diffusion-limited aggregation. phPhys. Rev. E. 64, (2001). %Not on ?
  • [105] Durang, X., Fortin, J-Y., Henkel, M.: Exact two-time correlation and response functions in the one-dimensional coagulation-diffusion process by the empty-interval method. phJournal of Statistical Mechanics: Theory and Experiment, (2011), P02030. %Not on
  • Felderhof, B. U.: Reports on Mathematical Physics 1, (1970), p 215 and 2, (1971), p151-152. %Not on ?
  • Glauber, Roy J. Time-dependent statistics of the Ising model. J. Mathematical Phys. 4 1963 294–307.
  • Petrov, Leonid. Pfaffian stochastic dynamics of strict partitions. Electron. J. Probab. 16 (2011), no. 82, 2246–2295.
  • Encyclopedia of mathematical physics. Vol. 1, 2, 3, 4, 5. Edited by Jean-Pierre Françoise, Gregory L. Naber and Tsou Sheung Tsun. Academic Press/Elsevier Science, Oxford, 2006. Vol. 1: l+679 pp.; Vol. 2: l+729 pp.; Vol 3: l+645 pp.; Vol. 4: l+673 pp.; Vol. 5: l+549 pp. ISBN: 978-0-1251-2660-1; 0-12-512660-3
  • Tribe, Roger; Zaboronski, Oleg. Pfaffian formulae for one dimensional coalescing and annihilating systems. Electron. J. Probab. 16 (2011), no. 76, 2080–2103.