Electronic Journal of Probability

The iPod Model

Daniel Lanoue

Full-text: Open access

Abstract

We introduce a Voter Model variant, inspired by social evolution of musical preferences. In our model, agents have preferences over a set of songs and upon meeting update their own preferences incrementally towards those of the other agents they meet. Using the spectral gap of an associated Markov chain, we give a geometry dependent result on the asymptotic consensus time of the model.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 64, 20 pp.

Dates
Accepted: 12 June 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067170

Digital Object Identifier
doi:10.1214/EJP.v20-3559

Mathematical Reviews number (MathSciNet)
MR3361252

Zentralblatt MATH identifier
1321.60212

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

Keywords
Markov Chains Stochastic Social Dynamics

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Lanoue, Daniel. The iPod Model. Electron. J. Probab. 20 (2015), paper no. 64, 20 pp. doi:10.1214/EJP.v20-3559. https://projecteuclid.org/euclid.ejp/1465067170


Export citation

References

  • Aldous, David. Interacting particle systems as stochastic social dynamics. Bernoulli 19 (2013), no. 4, 1122–1149.
  • Aldous, David; Lanoue, Daniel. A lecture on the averaging process. Probab. Surv. 9 (2012), 90–102.
  • Claudio Castellano, Santo Fortunato, and Vittorio Loreto. Statistical physics of social dynamics. Rev. Mod. Phys., 81:591–646, May 2009.
  • Cox, J. T. Coalescing random walks and voter model consensus times on the torus in ${\bf Z}^ d$. Ann. Probab. 17 (1989), no. 4, 1333–1366.
  • Dubins, Lester E. On a theorem of Skorohod. Ann. Math. Statist. 39 1968 2094–2097.
  • Durrett, Rick. Probability models for DNA sequence evolution. Probability and its Applications (New York). Springer-Verlag, New York, 2002. viii+240 pp. ISBN: 0-387-95435-X.
  • Levin, David A.; Peres, Yuval; Wilmer, Elizabeth L. Markov chains and mixing times. With a chapter by James G. Propp and David B. Wilson. American Mathematical Society, Providence, RI, 2009. xviii+371 pp. ISBN: 978-0-8218-4739-8
  • Oliveira, Roberto Imbuzeiro. Mean field conditions for coalescing random walks. Ann. Probab. 41 (2013), no. 5, 3420–3461.