Teil der Reihe: Mathematics and Statistics (R0)

Kinetically Constrained Models

Name: Kinetically Constrained Models
Brand: Ivailo Hartarsky
SKU: 9783031931154
Price: 53.49 EUR
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Inhaltsangabe

Preface.- The models.- Setting and notation.- The Markov processes: kinetically constrained spin models and kinetically constrained lattice gases.- The most studied choices of constraints.- Some useful classification: oriented/non–oriented models, cooperative/non–cooperative models.- Motivations from physics.- A crash course on liquid/glass and jamming transitions.- The quest of the ideal glass transition: models on Bethe lattices and the spiral model.- Kinetically Constrained Spin Models: the basic results.- Ergodicity and connection with bootstrap percolation.- Exponential convergence to equilibrium in L2.- The failure of classic coercive inequalities (logarithmic and modified logarithmic Sobolev constant).- Persistence and exchange times.- Scaling with density of the spectral gap: the case of Friedrickson-Andersen 1f model.- Some open problems.- Kinetically Constrained Spin Models on trees.- A martingale technique to prove positivity of the spectral gap.- Power law scaling at criticality.- An open problem.- The out of equilibrium regime.- An easy perturbative result in one dimension.- Oriented models: East and models on trees.- Non cooperative models.- Some open problems.- Dynamical phase transition.- Activity and its large deviations.- The one dimensional case: finite size effects and surface tension.- Open problems.- The East model.- Combinatorics.- Spectral gap and mixing time.- Time scale separation.- Front motion and cut-off.- Plateau behavior, aging and scaling limits.- The generalized East process in higher dimensions.- An open problem: Aldous Diaconis conjecture.- Kinetically Constrained Lattice Gases.- Ergodicity.- Non cooperative models: spectral gap, log-Sobolev, tagged particle and hydrodynamic limit.- Cooperative models: spectral gap and polynomial decay to equilibrium.

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