Large-Time Behavior of Finite-State Mean-Field Systems With Multiclasses

References

• Benaïm M, Le Boudec J-Y (2008) A class of mean field interaction models for computer and communication systems. Perform. Eval. 65(11–12):823–838.Google Scholar
• Billingsley P (1999) Convergence of Probability Measures (John Wiley & Sons, New York).Google Scholar
• Biswas A, Borkar V (2011) Small noise asymptotics for invariant densities for a class of diffusions: A control theoretic view (with erratum). Preprint, submitted, https://arxiv.org/abs/1107.2277.Google Scholar
• Borkar V, Sundaresan R (2012) Asymptotics of the invariant measure in mean field models with jumps. Stoch. Syst. 2(2):322–380.Link, Google Scholar
• Bouchet F, Gawȩdzki K, Nardini C (2016) Perturbative calculation of quasi-potential in non-equilibrium diffusions: A mean-field example. J. Stat. Phys. 163:1157–1210.Google Scholar
• Chong C, Klüppelberg C (2019) Partial mean field limits in heterogeneous networks. Stochastic Process. Appl. 129:4998–5036.Google Scholar
• Collet F (2014) Macroscopic Limit of a bipartite Curie-Weiss model: A dynamical approach. J. Stat. Phys. 157:1309–1319.Google Scholar
• Collet F, Formentin M, Tovazzi D (2016) Rhythmic behavior in a two-population mean-field Ising model. Phys. Rev. E. 94:042139.Google Scholar
• Cox J, Greven A (1990) On the long term behavior of some finite particle systems. Probab. Theory Related Fields 85:195–237.Google Scholar
• Dawson D, Gärtner J (1987) Large deviations from the McKean-Vlasov limit for weakly interacting diffusions. Stochastics 20(4):247–308.Google Scholar
• Dawson D, Gärtner J (1989) Large deviations, free energy functional and quasipotential for a mean field model of interacting diffusions. Mem. Amer. Math. Soc. 78(398).Google Scholar
• Dawson D, Greven A (1993) Hierarchical models of interacting diffusions: Multiple time scale phenomena, phase transition, and pattern of cluster-formation. Probab. Theory Related Fields 96:435–473.Google Scholar
• Dawson D, Greven A (1999) Hierarchically interacting Fleming-Viot processes with selection and mutation: Multiple space time scale analysis and quasi-equilibria. Electron. J. Probab. 4:1–81.Google Scholar
• Dawson D, Greven A, Vaillancourt J (1995) Equilibria and quasi-equilibria for infinite collections of interacting Fleming-Viot processes. Trans. Amer. Math. Soc. 347(7):2277–2360.Google Scholar
• Dawson D, Sid-Ali A, Zhao Y (2020) Propagation of chaos and large deviations in mean-field models with jumps on block-structured networks. Preprint, submitted December 4, https://arxiv.org/abs/2012.02870.Google Scholar
• Dembo A, Zeitouni O (2010) Large Deviations Techniques and Applications, 2nd ed. (Springer, New York).Google Scholar
• Döring L, Mytnik L (2013) Longtime Behavior for Mutually Catalytic Branching with Negative Correlations, vol. 38 (Springer Proceedings in Mathematics & Statistics, Boston).Google Scholar
• Feng J, Kurtz T (2006) Large Deviations for Stochastic Processes (Mathematical Surveys and Monographs, American Mathematical Society).Google Scholar
• Feng S (1994) Large deviations for empirical process of mean-field interacting particle system with unbounded jumps. Ann. Probab. 22(4):2122–2151.Google Scholar
• Freidlin M, Wentzell A (2012) Random Perturbations of Dynamical Systems, 3rd ed. (Springer, Berlin-Heidelberg).Google Scholar
• Graham C (2008) Chaoticity for multiclass systems and exchangeability within classes. J. Appl. Probab. 45:1196–1203.Google Scholar
• Greven A, den Hollander F (2007) Phase transitions for the long-time behavior of interacting diffusions. Ann. Probab. 35(4):1250–1306.Google Scholar
• Hwang C, Sheu S (1990) Large-time behavior of perturbed diffusion Markov processes with applications to the second eigenvalue problem for Fokker-Planck operators and simulated annealing. Acta Appl. Math. 19:253–295.Google Scholar
• Knöpfel H, Löwe M, Schubert K, Sinulis A (2020) Fluctuation results for general block spin Ising models. J. Stat. Phys. 178(1):1175–1200.Google Scholar
• Kuehn C (2015) Multiple Time Scale Dynamics (Springer International Publishing, Switzerland).Google Scholar
• Léonard C (1995a) Large deviations for long range interacting particle systems with jumps. Annales de l’I.H.P. Probabilités et Statistiques, Tome 31 31(2):289–323.Google Scholar
• Léonard C (1995b) On large deviations for particle systems associated with spatially homogeneous Boltzmann type equations. Probab. Theory Related Fields 101:1–44.Google Scholar
• Meylahn JM (2020) Two-community noisy Kuramoto model. Nonlinearity 33(4):1847–1880.Google Scholar
• Nguyen DT, Nguyen S, Du N (2020) On mean field systems with multi-classes. Discrete Contin. Dyn. Syst. 40(2):683–707.Google Scholar
• Tang Y, Yuan R, Wang G, Zhu X, Ao P (2017) Potential landscape of high dimensional nonlinear stochastic dynamics with large noise. Sci. Rep. 7(15762):1157–1210.Google Scholar
• Yasodharan S, Sundaresan R (2019) Large time behaviour and the second eigenvalue problem for finite state mean-field interacting particle systems. Preprint, submitted September 9, https://arxiv.org/abs/1909.03805.Google Scholar
• Yasodharan S, Sundaresan R (2021) A sufficient condition for the quasipotential to be the rate function of the invariant measure of countable-state mean-field interacting particle systems. Preprint, submitted October 25, https://arxiv.org/abs/2110.12640.Google Scholar
• Zhou J, Aliyu M, Aurell E, Huang S (2012) Quasi-potential landscape in complex multi-stable systems. R. Soc. Interface 9:3539–3553.Google Scholar