Мақаланы E-mail арқылы жіберу Invariant measures for contact processes with state-dependent birth and death rates
- Авторлар: Zhizhina E.1, Pirogov S.1
-
Мекемелер:
- Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences
- Шығарылым: Том 59, № 2 (2023)
- Беттер: 63-82
- Бөлім: Articles
- URL: https://journals.rcsi.science/0555-2923/article/view/247409
- DOI: https://doi.org/10.31857/S0555292323020055
- EDN: https://elibrary.ru/PQGTBP
- ID: 247409
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Аннотация
We consider contact processes on locally compact separable metric spaces with birth and death rates that are heterogeneous in space. We formulate conditions on the rates that ensure the existence of invariant measures of contact processes. One of the crucial conditions is the so-called critical regime condition. To prove the existence of invariant measures, we use the approach proposed in our preceding paper. We discuss in detail the multi-species contact model with a compact space of marks (species) in which both birth and death rates depend on the marks.
Авторлар туралы
E. Zhizhina
Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences
Email: ejj@iitp.ru
Moscow, Russia
S. Pirogov
Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences
Email: s.a.pirogov@bk.ru
Moscow, Russia
Әдебиет тізімі
- Harris T.E. Contact Interactions on a Lattice // Ann. Probab. 1974. V. 2. № 6. P. 969-988. https://doi.org/10.1214/aop/1176996493
- Holley R., Liggett T.M. The Survival of Contact Processes // Ann. Probab. 1978. V. 6. № 2. P. 198-206. https://doi.org/10.1214/aop/1176995567
- Liggett T.M.Interacting Particle Systems. New York: Springer-Verlag, 1985.
- Kondratiev Yu., Kutoviy O., Pirogov S. Correlation Functions and Invariant Measures in Continuous Contact Model // Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2008. V. 11. № 2. P. 231-258. https://doi.org/10.1142/S0219025708003038
- Kondratiev Yu.G., Kutoviy O.V., Pirogov S.A., Zhizhina E. Invariant Measures for Spatial Contact Model in Small Dimensions // Markov Process. Related Fields. 2021. V. 27. № 3. P. 413-438. https://math-mprf.org/journal/articles/id1616
- Kondratiev Yu., Skorokhod A. On Contact Processes in Continuum // Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2006. V. 9. № 2. P. 187-198. https://doi.org/10.1142/S0219025706002305
- Kondratiev Yu., Pirogov S., Zhizhina E. A Quasispecies Continuous Contact Model in a Critical Regime // J. Stat. Phys. 2016. V. 163. № 2. P. 357-373. https://doi.org/10.1007/s10955-016-1480-5
- Pirogov S., Zhizhina E., A Quasispecies Continuous Contact Model in a Subcritical Regime // Moscow Math. J. 2019. V. 19. № 1. P. 121-132. https://doi.org/10.17323/1609-4514-2019-19-1-121-132
- Nowak M. What Is a Quasispecies? // Trends Ecol. Evol. 1992. V. 7. № 4. P. 118-121. https://doi.org/10.1016/0169-5347(92)90145-2
- Pirogov S., Zhizhina E. Contact Processes on General Spaces. Models on Graphs and on Manifolds // Electron. J. Probab. 2022. V. 27. Article no. 41 (14 pp.). doi.org/10.1214/22-EJP765
- Ruelle D. Statistical Mechanics: Rigorous Results. New York: Benjamin, 1969.
- Lenard A. Correlation Functions and the Uniqueness of the State in Classical Statistical Mechanics // Commun. Math. Phys. 1973. V. 30. № 1. P. 35-44. https://doi.org/10.1007/BF01646686
- Lenard A. States of Classical Statistical Mechanical Systems of Infinitely Many Particles. II. Characterization of Correlation Measures // Arch. Rational Mech. Anal. 1975. V. 59. № 3. P. 241-256. https://doi.org/10.1007/BF00251602
- Petrov V.V. Limit Theorems of Probability Theory: Sequences of Independent Random Variables. Oxford: Clarendon; New York: Oxford Univ. Press, 1995.
