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Stein’s Method and a Cubic Mean-Field Model Stein方法和三次平均场模型
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-12-05 DOI: 10.1007/s10955-024-03373-x
Peter Eichelsbacher
{"title":"Stein’s Method and a Cubic Mean-Field Model","authors":"Peter Eichelsbacher","doi":"10.1007/s10955-024-03373-x","DOIUrl":"10.1007/s10955-024-03373-x","url":null,"abstract":"<div><p>In this paper, we study a mean-field spin model with three- and two-body interactions. In a recent paper (Ann Henri Poincaré, 2024) by Contucci, Mingione and Osabutey, the equilibrium measure for large volumes was shown to have three pure states, two with opposite magnetization and an unpolarized one with zero magnetization, merging at the critical point. The authors proved a central limit theorem for the suitably rescaled magnetization. The aim of our paper is presenting a prove of a central limit theorem for the rescaled magnetization applying the exchangeable pair approach due to Stein. Moreover we prove (non-uniform) Berry–Esseen bounds, a concentration inequality, Cramér-type moderate deviations and a moderate deviations principle for the suitably rescaled magnetization. Interestingly we analyze Berry–Esseen bounds in case the model-parameters <span>((K_n,J_n))</span> converge to the critical point (0, 1) on lines with different slopes and with a certain speed, and obtain new limiting distributions and thresholds for the speed of convergence.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03373-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142778202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some Rigorous Results for the Diluted Multi-species SK Model 稀释多物种SK模型的一些严格结果
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-12-03 DOI: 10.1007/s10955-024-03376-8
Qun Liu, Zhishan Dong
{"title":"Some Rigorous Results for the Diluted Multi-species SK Model","authors":"Qun Liu,&nbsp;Zhishan Dong","doi":"10.1007/s10955-024-03376-8","DOIUrl":"10.1007/s10955-024-03376-8","url":null,"abstract":"<div><p>We consider the diluted multi-species Sherrington–Kirkpatrick (DMSK) model in which the variance of disorders depend on the species the particles belong to, and the number of edges within each block is diluted. First, we find the annealed region of the DMSK model at high temperature and compute the corresponding free energy. Next, we get a fluctuation result for the overlap vector through a differential method. Lastly, by using cavity method, we obtain the corresponding replica symmetric bound and r-step of replica symmetry breaking bound.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142762019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hierarchical Cubes: Gibbs Measures and Decay of Correlations 分层立方体：吉布斯测量和相关性衰减
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-28 DOI: 10.1007/s10955-024-03375-9
Sabine Jansen, Jan Philipp Neumann
{"title":"Hierarchical Cubes: Gibbs Measures and Decay of Correlations","authors":"Sabine Jansen,&nbsp;Jan Philipp Neumann","doi":"10.1007/s10955-024-03375-9","DOIUrl":"10.1007/s10955-024-03375-9","url":null,"abstract":"<div><p>We study a hierarchical model of non-overlapping cubes of sidelengths <span>(2^j)</span>, <span>(jin {mathbb {Z}})</span>. The model allows for cubes of arbitrarily small size and the activities need not be translationally invariant. It can also be recast as a spin system on a tree with a long-range hard-core interaction. We prove necessary and sufficient conditions for the existence and uniqueness of Gibbs measures, discuss fragmentation and condensation, and prove bounds on the decay of two-point correlation functions.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03375-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Large Deviation Principle for Nonlinear Stochastic Wave Equation Driven by Rough Noise 粗糙噪声驱动的非线性随机波方程的大偏差原理
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-26 DOI: 10.1007/s10955-024-03371-z
Ruinan Li, Beibei Zhang
{"title":"A Large Deviation Principle for Nonlinear Stochastic Wave Equation Driven by Rough Noise","authors":"Ruinan Li,&nbsp;Beibei Zhang","doi":"10.1007/s10955-024-03371-z","DOIUrl":"10.1007/s10955-024-03371-z","url":null,"abstract":"<div><p>This paper is devoted to investigating Freidlin–Wentzell’s large deviation principle for one (spatial) dimensional nonlinear stochastic wave equation <span>(frac{partial ^2 u^{{varepsilon }}(t,x)}{partial t^2}=frac{partial ^2 u^{{varepsilon }}(t,x)}{partial x^2}+sqrt{{varepsilon }}sigma (t, x, u^{{varepsilon }}(t,x))dot{W}(t,x))</span>, where <span>(dot{W})</span> is white in time and fractional in space with Hurst parameter <span>(Hin big (frac{1}{4},frac{1}{2}big ))</span>. The variational framework and the modified weak convergence criterion proposed by Matoussi et al. (Appl Math Optim 83(2):849–879, 2021) are adopted here.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamics of the Infinite Discrete Nonlinear Schrödinger Equation 无限离散非线性薛定谔方程的动力学原理
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-26 DOI: 10.1007/s10955-024-03374-w
Aleksis Vuoksenmaa
{"title":"Dynamics of the Infinite Discrete Nonlinear Schrödinger Equation","authors":"Aleksis Vuoksenmaa","doi":"10.1007/s10955-024-03374-w","DOIUrl":"10.1007/s10955-024-03374-w","url":null,"abstract":"<div><p>The discrete nonlinear Schrödinger equation on <span>({mathbb Z}^d)</span>, <span>(d ge 1)</span> is an example of a dispersive nonlinear wave system. Being a Hamiltonian system that conserves also the <span>(ell ^2({mathbb Z}^d))</span>-norm, the well-posedness of the corresponding Cauchy problem follows for square-summable initial data. In this paper, we prove that the well-posedness continues to hold for initial data that can grow towards infinity, namely anything that has at most a certain power law growth far away from the origin. The growth condition is loose enough to guarantee that, at least in dimension <span>(d=1)</span>, initial data sampled from any reasonable equilibrium distribution of the defocusing DNLS satisfies it almost surely.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03374-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov–Poisson 量子优化传输伪计量学中的增强稳定性：从哈特里到弗拉索夫-泊松
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-25 DOI: 10.1007/s10955-024-03367-9
Mikaela Iacobelli, Laurent Lafleche
{"title":"Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov–Poisson","authors":"Mikaela Iacobelli,&nbsp;Laurent Lafleche","doi":"10.1007/s10955-024-03367-9","DOIUrl":"10.1007/s10955-024-03367-9","url":null,"abstract":"<div><p>In this paper we establish almost-optimal stability estimates in quantum optimal transport pseudometrics for the semiclassical limit of the Hartree dynamics to the Vlasov–Poisson equation, in the regime where the solutions have bounded densities. We combine Golse and Paul’s method from [Arch Ration Mech Anal 223:57–94, 2017], which uses a semiclassical version of the optimal transport distance and which was adapted to the case of the Coulomb and gravitational interactions by the second author in [J Stat Phys 177:20–60, 2019], with a new approach developed by the first author in [Arch Ration Mech Anal 244:27–50, 2022] to quantitatively improve stability estimates in kinetic theory.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03367-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relativistic One-Dimensional Billiards 相对论一维台球
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-25 DOI: 10.1007/s10955-024-03364-y
Alfonso Artigue
{"title":"Relativistic One-Dimensional Billiards","authors":"Alfonso Artigue","doi":"10.1007/s10955-024-03364-y","DOIUrl":"10.1007/s10955-024-03364-y","url":null,"abstract":"<div><p>In this article we study the dynamics of one-dimensional relativistic billiards containing particles with positive and negative energy. We study configurations with two identical positive masses and symmetric positions with two massless particles between them of negative energy and symmetric positions. We show that such systems have finitely many collisions in any finite time interval. This is due to a phenomenon we call <i>tachyonic collision</i>, which occur at small scales and produce changes in the sign of the energy of individual particles. We also show that depending on the initial parameters the solutions can be bounded with certain periodicity or unbounded while obeying an inverse square law at large distances.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Pirogov–Sinai Theory for Infinite Interactions 无限相互作用的皮罗戈夫-西奈理论
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-25 DOI: 10.1007/s10955-024-03370-0
A. Mazel, I. Stuhl, Y. Suhov
{"title":"The Pirogov–Sinai Theory for Infinite Interactions","authors":"A. Mazel,&nbsp;I. Stuhl,&nbsp;Y. Suhov","doi":"10.1007/s10955-024-03370-0","DOIUrl":"10.1007/s10955-024-03370-0","url":null,"abstract":"<div><p>The purpose of this note is to consider a number of straightforward generalizations of the Pirogov–Sinai theory which can be covered by minor additions to the canonical texts. These generalizations are well-known among the adepts of the Pirogov–Sinai theory but are lacking formal references.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geometric Aspects of a Spin Chain 自旋链的几何方面
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-25 DOI: 10.1007/s10955-024-03332-6
Michael Entov, Leonid Polterovich, Lenya Ryzhik
{"title":"Geometric Aspects of a Spin Chain","authors":"Michael Entov,&nbsp;Leonid Polterovich,&nbsp;Lenya Ryzhik","doi":"10.1007/s10955-024-03332-6","DOIUrl":"10.1007/s10955-024-03332-6","url":null,"abstract":"<div><p>We discuss non-equilibrium thermodynamics of the mean-field Ising model from a geometric perspective, focusing on the thermodynamic limit. When the number of spins is finite, the Gibbs equilibria form a smooth Legendrian submanifold in the thermodynamic phase space whose points describe the stable macroscopic states of the system. We describe the convergence of these smooth Legendrian submanifolds, as the number of spins goes to infinity, to a singular Legendrian submanifold, admitting an analytic continuation that contains both the stable and metastable states. We also discuss the relaxation to a Gibbs equilibrium when the physical parameters are changed abruptly. The relaxation is defined via the gradient flow of the free energy with respect to the Wasserstein metric on microscopic states, that is, in the geometric language, via the gradient flow of the generating function of the equilibrium Legendrian with respect to the ghost variables. This leads to a discrete Fokker-Planck equation when the number of spins is finite. We show that in the thermodynamic limit this description is closely related to the seminal model of relaxation proposed by Glauber. Finally, we find a special range of parameters where such relaxation happens instantaneously, along the Reeb chords connecting the initial and the terminal Legendrian submanifolds.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Propagation of Chaos and Phase Transition in a Stochastic Model for a Social Network 社交网络随机模型中的混沌传播与相变
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-25 DOI: 10.1007/s10955-024-03365-x
Eva Löcherbach, Kádmo Laxa
{"title":"Propagation of Chaos and Phase Transition in a Stochastic Model for a Social Network","authors":"Eva Löcherbach,&nbsp;Kádmo Laxa","doi":"10.1007/s10955-024-03365-x","DOIUrl":"10.1007/s10955-024-03365-x","url":null,"abstract":"<div><p>We consider a model for a social network with N interacting social actors. This model is a system of interacting marked point processes in which each point process indicates the successive times in which a social actor expresses a “favorable” (<span>(+1)</span>) or “contrary” (<span>(-1)</span>) opinion. The orientation and the rate at which an actor expresses an opinion is influenced by the social pressure exerted on this actor. The social pressure of an actor is reset to 0 when the actor expresses an opinion, and simultaneously the social pressures on all the other actors change by h/N in the direction of the opinion that was just expressed. We prove propagation of chaos of the system, as N diverges to infinity, to a limit nonlinear jumping stochastic differential equation. Moreover, we prove that under certain conditions the limit system exhibits a phase transition described as follows. If h is smaller or equal than a certain threshold, the limit system has only the null Dirac measure as an invariant probability measure, corresponding to a vanishing social pressure on all actors. However, if h is greater than the threshold, the system has two additional non-trivial invariant probability measures. One of these measures has support on the positive real numbers and the other is obtained by symmetrization with respect to 0, having thus support on the negative real numbers.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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