Second time scale of the metastability of reversible inclusion processes

Correction: Second time scale of the metastability of reversible inclusion processes

“…We also demonstrate that there are no other meaningful time scales except the three identified ones. This work completes the verification of the conjecture made in [7] which was partially resolved on the first time scale in [7] and on the second time scale in [25]. Main tools are potential-theoretic approach and martingale approach to metastability; we thoroughly investigate the highly-complicated energy landscape of the system to construct suitable test objects to provide sharp asymptotics on capacities.…”

“…The authors justified the argument by demonstrating it on one-dimensional simple geometry. This conjecture was partially proved in [25] regarding the second time scale θ 2 , in that for any underlying geometry of particle movements, the θ 2 -accelerated inclusion process converges to a new scaling limit process, which is still not necessarily irreducible. Thus, it was also conjectured in [25] that there remains one more time scale.…”

“…In the context of statistical physics, metastability corresponds to the so-called first-order phase transition, in that certain observables of a system exhibit discontinuity with respect to the intensive variables of the system. Typical examples are found in small random perturbations of dynamical systems [9-11, 38, 39, 43], interacting particle systems with sticky interactions [7,23,25,26,31,32], ferromagnetic spin systems in low temperatures [5,15,27,40,41], etc. From a dynamical point of view, metastability can be explained as follows.…”

Metastable $Γ$-expansion of finite state Markov chains level two large deviations rate functions

“…This includes random walks in potential fields [39,41], condensing zero-range models [2,31,53], inclusion processes [25,17,9,27,28], or statistical mechanical models in which the volume grows as the temperature decreases. For example, the Curie-Weiss model in random environment [11,10], the Blume-Capel model [34], the Potts model [40,30,44], or the Kawasaki dynamics for the Ising model [24].…”

Metastability of Blume-Capel model with zero chemical potential and zero external field

“…Extensive research has been carried out on metastability since the mid-20th century, ranging from the early works [6,7] to recently developed methodologies [1][2][3]17]. As a result, various stochastic systems have been known to exhibit such behavior; important examples include the small random perturbations of dynamical systems [6,18,25], condensing interacting particle systems [12,13,17,26], and ferromagnetic spin systems at low temperatures [4,10,15,16,21,23]. We refer to the classic monographs [5,24] for detailed explanation on the history and perspectives regarding the phenomenon of metastability.…”