Misturini, Ricardo Evolution of the ABC model among the segregated configurations in the zero-temperature limit. (English. French summary) Zbl 1342.60174 Ann. Inst. Henri Poincaré, Probab. Stat. 52, No. 2, 669-702 (2016). Summary: We consider the ABC model on a ring in a strongly asymmetric regime. The main result asserts that the particles almost always form three pure domains (one of each species) and that this segregated shape evolves, in a proper time scale, as a Brownian motion on the circle, which may have a drift. This is, to our knowledge, the first proof of a zero-temperature limit for non-reversible dynamics whose invariant measure is not explicitly known. Cited in 3 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60J65 Brownian motion 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics 82C22 Interacting particle systems in time-dependent statistical mechanics Keywords:ABC model; scaling limits; Brownian motion; metastability; tunneling PDF BibTeX XML Cite \textit{R. Misturini}, Ann. Inst. Henri Poincaré, Probab. Stat. 52, No. 2, 669--702 (2016; Zbl 1342.60174) Full Text: DOI Euclid arXiv References: [1] J. Beltrán and C. Landim. Tunneling and metastability of continuous time Markov chains. J. Stat. Phys. 140 (2010) 1065-1114. · Zbl 1223.60061 · doi:10.1007/s10955-010-0030-9 · arxiv:0910.4088 [2] J. Beltrán and C. Landim. Tunneling of the Kawasaki dynamics at low temperatures in two dimensions. Ann. Inst. Henri Poincaré Probab. Stat. 51 (2015) 59-88. · Zbl 1314.82036 · doi:10.1214/13-AIHP568 · euclid:aihp/1421244399 [3] M. Clincy, B. Derrida and M. R. Evans. Phase transition in the ABC model. Phys. Rev. E (3) 67 066115 (2003). · doi:10.1103/PhysRevE.67.066115 [4] R. Durrett. Stochastic Calculus: A Practical Introduction. Probability and Stochastics Series . CRC Press, Boca Raton, 1996. · Zbl 0856.60002 [5] M. R. Evans, Y. Kafri, H. M. Koduvely and D. Mukamel. Phase separation in one-dimensional driven diffusive systems. Phys. Rev. Lett. 80 (1998) 425-429. [6] M. R. Evans, Y. Kafri, H. M. Koduvely and D. Mukamel. Phase separation and coarsening in one-dimensional driven diffusive systems: Local dynamics leading to long-range Hamiltonians. Phys. Rev. E (3) 58 (1998) 2764-2778. · doi:10.1103/PhysRevE.58.2764 [7] B. Gois and C. Landim. Zero-temperature limit of the Kawasaki dynamics for the Ising lattice gas in a large two-dimensional torus. Ann. Probab. 43 (2015) 2151-2203. · Zbl 1326.60137 · doi:10.1214/14-AOP930 · euclid:aop/1433341329 · arxiv:1305.4542 [8] C. Landim. A topology for limits of Markov chains. Stochastic Process. Appl. 125 (2015) 1058-1088. · Zbl 1322.60153 · doi:10.1016/j.spa.2014.08.011 · arxiv:1310.3646 [9] E. Olivieri and E. Scoppola. Markov chains with exponentially small transition probabilities: First exit problem from general domain II. The general case. J. Stat. Phys. 84 (1996) 987-1041. · Zbl 1081.60542 · doi:10.1007/BF02174126 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.