Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees : Applications to Non-Archimedean Diophantine Approximation / / by Anne Broise-Alamichel, Jouni Parkkonen, Frédéric Paulin

• Record Nr.: UNINA9910364957603321
• Autore: Broise-Alamichel Anne
• Pubbl/distr/stampa: Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2019
• ISBN: 3-030-18315-7
• Edizione: [1st ed. 2019.]
• Descrizione fisica: 1 online resource (viii, 413 pages) : illustrations
• Collana: Progress in Mathematics, , 0743-1643 ; ; 329
• Disciplina: 516.362
• Soggetti: Dynamics; Ergodic theory; Geometry, Differential; Group theory; Number theory; Convex geometry; Discrete geometry; Probabilities; Dynamical Systems and Ergodic Theory; Differential Geometry; Group Theory and Generalizations; Number Theory; Convex and Discrete Geometry; Probability Theory and Stochastic Processes
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Introduction -- Negatively curved geometry -- Potentials, critical exponents and Gibbs cocycles -- Patterson-Sullivan and Bowen-Margulis measures with potential on CAT(-1) spaces -- Symbolic dynamics of geodesic flows on trees -- Random walks on weighted graphs of groups -- Skinning measures with potential on CAT(-1) spaces -- Explicit measure computations for simplicial trees and ; graphs of groups -- Rate of mixing for the geodesic flow -- Equidistribution of equidistant level sets to Gibbs measures -- Equidistribution of common perpendicular arcs -- Equidistribution and counting of common perpendiculars in quotient spaces -- Geometric applications -- Fields with discrete valuations -- Bruhat-Tits trees and modular groups -- Rational point equidistribution and counting in completed function fields -- Equidistribution and counting of quadratic irrational points in non-Archimedean local fields -- Counting and equidistribution of crossratios -- Counting and equidistribution of integral representations by quadratic norm forms -- A - A weak Gibbs measure is the unique equilibrium, by J. Buzzi -- List of Symbols -- Index -- Bibliography.
• Sommario/riassunto: This book provides a complete exposition of equidistribution and counting problems weighted by a potential function of common perpendicular geodesics in negatively curved manifolds and simplicial trees. Avoiding any compactness assumptions, the authors extend the theory of Patterson-Sullivan, Bowen-Margulis and Oh-Shah (skinning) measures to CAT(-1) spaces with potentials. The work presents a proof for the equidistribution of equidistant hypersurfaces to Gibbs measures, and the equidistribution of common perpendicular arcs between, for instance, closed geodesics. Using tools from ergodic theory (including coding by topological Markov shifts, and an appendix by Buzzi that relates weak Gibbs measures and equilibrium states for them), the authors further prove the variational principle and rate of mixing for the geodesic flow on metric and simplicial trees—again without the need for any compactness or torsionfree assumptions. In a series of applications, using the Bruhat-Tits trees over non-Archimedean local fields, the authors subsequently prove further important results: the Mertens formula and the equidistribution of Farey fractions in function fields, the equidistribution of quadratic irrationals over function fields in their completions, and asymptotic counting results of the representations by quadratic norm forms. One of the book's main benefits is that the authors provide explicit error terms throughout. Given its scope, it will be of interest to graduate students and researchers in a wide range of fields, for instance ergodic theory, dynamical systems, geometric group theory, discrete subgroups of locally compact groups, and the arithmetic of function fields.

Constitutional rights after globalization / Gavin W. Anderson

• Record Nr.: UNINA9910961739603321
• Autore: Anderson Gavin W.
• Pubbl/distr/stampa: Oxford ; Portland, Ore., : Hart Publishing, 2005
• ISBN: 9786610801299; 9781472559715; 1472559711; 9781280801297; 1280801298; 9781847312457; 1847312454
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (170 p.)
• Disciplina: 342.02
• Soggetti: Human rights; Constitutional law; Human rights and globalization; Legal polycentricity
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index
• Nota di contenuto: Part One: Constitutionalism beyond the State -- 1: Constitutionalism in an Age of Globalisation -- 2: Globalisation and the Reconfiguration of Political Power -- Part Two: Rights Constitutionalism and the Challenge of Legal Pluralism -- 3: The Paradigmatic Debate: Liberal Legalism and Legal Pluralism -- 4: Internal Legal Pluralism and the Interpretive Question -- 5: External Legal Pluralism and the Instrumental Question -- Part Three: Constitutional Rights in an Age of Globalisation: Towards a Legal Pluralist Theory of Constitutionalism -- 6: Legal Pluralism and the Politics of Constitutional Definition -- 7: Rights Constitutionalism and the Counterhegemonic Difficulty -- Conclusion: Towards a Legal Pluralist Constitutionalism
• Sommario/riassunto: Constitutional Rights after Globalization juxtaposes the globalization of the economy and the worldwide spread of constitutional charters of rights. The shift of political authority to powerful economic actors ; entailed by neo-liberal globalization challenges the traditional state-centred focus of constitutional law. Contemporary debate has responded to this challenge in normative terms, whether by reinterpreting rights or redirecting their ends, e.g. to reach private actors. However, globalization undermines the liberal legalist epistemology on which these approaches rest, by positing the existence of multiple sites of legal production, (e.g. multinational corporations) beyond the state. This dynamic, between globalization and legal pluralism on one side, and rights constitutionalism on the other, provides the context for addressing the question of rights constitutionalism's counterhegemonic potential. This shows first that the interpretive and instrumental assumptions underlying constitutional adjudication are empirically suspect: constitutional law tends more to disorder than coherence, and frequently is an ineffective tool for social change. Instead, legal pluralism contends that constitutionalism's importance lies in symbolic terms as a legitimating discourse. The competing liberal and 'new' politics of definition (the latter highlighting how neoliberal values and institutions constrain political action) are contrasted to show how each advances different agenda. A comparative survey of constitutionalism's engagement with private power shows that conceiving of constitutions in the predominant liberal, legalist mode has broadly favoured hegemonic interests. It is concluded that counterhegemonic forms of constitutional discourse cannot be effected within, but only by unthinking, the dominant liberal legalist paradigm, in a manner that takes seriously all exercises of political power