TY - JOUR
T1 - Critical fluctuations in renewal models of statistical mechanics
AU - ZAMPARO, MARCO
PY - 2021
Y1 - 2021
N2 - We investigate the sharp asymptotic behavior at criticality of the large fluctuations of extensive observables in renewal models of statistical mechanics, such as the Poland-Scheraga model of DNA denaturation, the Fisher-Felderhof model of fluids, the Wako-Saitô-Muñoz-Eaton model of protein folding, and the Tokar-Dreyssé model of strained epitaxy. These models amount to Gibbs changes of measure of a classical renewal process and can be identified with a constrained pinning model of polymers. The extensive observables that enter the thermodynamic description turn out to be cumulative rewards corresponding to deterministic rewards that are uniquely determined by the waiting time and grow no faster than it. The probability decay with the system size of their fluctuations switches from exponential to subexponential at criticality, which is a regime corresponding to a discontinuous pinning-depinning phase transition. We describe such decay by proposing a precise large deviation principle under the assumption that the subexponential correction term to the waiting time distribution is regularly varying. This principle is, in particular, used to characterize the fluctuations of the number of renewals, which measures the DNA-bound monomers in the Poland-Scheraga model, the particles in the Fisher-Felderhof model and the Tokar-Dreyssé model, and the native peptide bonds in the Wako-Saitô-Muñoz-Eaton model.
AB - We investigate the sharp asymptotic behavior at criticality of the large fluctuations of extensive observables in renewal models of statistical mechanics, such as the Poland-Scheraga model of DNA denaturation, the Fisher-Felderhof model of fluids, the Wako-Saitô-Muñoz-Eaton model of protein folding, and the Tokar-Dreyssé model of strained epitaxy. These models amount to Gibbs changes of measure of a classical renewal process and can be identified with a constrained pinning model of polymers. The extensive observables that enter the thermodynamic description turn out to be cumulative rewards corresponding to deterministic rewards that are uniquely determined by the waiting time and grow no faster than it. The probability decay with the system size of their fluctuations switches from exponential to subexponential at criticality, which is a regime corresponding to a discontinuous pinning-depinning phase transition. We describe such decay by proposing a precise large deviation principle under the assumption that the subexponential correction term to the waiting time distribution is regularly varying. This principle is, in particular, used to characterize the fluctuations of the number of renewals, which measures the DNA-bound monomers in the Poland-Scheraga model, the particles in the Fisher-Felderhof model and the Tokar-Dreyssé model, and the native peptide bonds in the Wako-Saitô-Muñoz-Eaton model.
KW - N.A
KW - N.A
UR - https://iris.uniupo.it/handle/11579/173924
U2 - 10.1063/5.0049786
DO - 10.1063/5.0049786
M3 - Article
SN - 0022-2488
SP - 113301
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
ER -