LEADER 05717nam 22007335 450 001 9911015963303321 005 20260216155726.0 010 $a3-031-93115-7 024 7 $a10.1007/978-3-031-93115-4 035 $a(MiAaPQ)EBC32226514 035 $a(Au-PeEL)EBL32226514 035 $a(CKB)39672124900041 035 $a(DE-He213)978-3-031-93115-4 035 $a(EXLCZ)9939672124900041 100 $a20250719d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aKinetically Constrained Models /$fby Ivailo Hartarsky, Cristina Toninelli 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (240 pages) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1765 ;$v53 311 08$a3-031-93114-9 327 $aPreface -- 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. 330 $aThis book offers an in-depth review of kinetically constrained models (KCMs), a topic that lies at the crossroads of probability and statistical mechanics. KCMs have captivated physicists ever since their introduction in the 1980s. Their remarkable glassy behavior makes them an essential toy model for exploring the liquid?glass transition, a longstanding puzzle in condensed matter physics. Over the past 20 years, KCMs have also gained significant attention in mathematics. Despite belonging to the well-established domain of interacting particle systems with stochastic dynamics, the presence of dynamical constraints gives rise to novel phenomena. These include anomalously long mixing times, aging effects, singularities in the dynamical large deviation function, dynamical heterogeneities, and atypical ergodicity-breaking transitions corresponding to the emergence of a large variety of amorphous structures. Authored by two leading experts in the field, this volume offers an extensive overview of rigorous results in the field. The self-contained exposition, with emphasis on high-level ideas and common techniques, is suitable for novices, as well as seasoned researchers, with backgrounds in mathematics or physics. The text covers crucial connections to bootstrap percolation cellular automata, along with sharp thresholds, universality, out-of-equilibrium dynamics, and more. The volume features challenging open questions and a detailed bibliography to direct future research. Whether as a reference or a study guide, it is a valuable resource for those interested in KCM. 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1765 ;$v53 606 $aSystem theory 606 $aProbabilities 606 $aMathematical physics 606 $aComplex Systems 606 $aProbability Theory 606 $aMathematical Physics 606 $aMathematical Methods in Physics 606 $aTheoretical, Mathematical and Computational Physics 606 $aSistemes complexos$2thub 606 $aFísica matemàtica$2thub 606 $aProbabilitats$2thub 606 $aFísica$2thub 608 $aLlibres electrònics$2thub 615 0$aSystem theory. 615 0$aProbabilities. 615 0$aMathematical physics. 615 14$aComplex Systems. 615 24$aProbability Theory. 615 24$aMathematical Physics. 615 24$aMathematical Methods in Physics. 615 24$aTheoretical, Mathematical and Computational Physics. 615 7$aSistemes complexos 615 7$aFísica matemàtica 615 7$aProbabilitats 615 7$aFísica 676 $a530.1 700 $aHartarsky$b Ivailo$01834945 701 $aToninelli$b Cristina$01834946 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911015963303321 996 $aKinetically Constrained Models$94410636 997 $aUNINA