Titlebook: Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees; Applications to Non- Anne Broise-Alamichel,Jouni Pa

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Application of Bamboo in Building EnvelopeIn this chapter, we give background information and preliminary results on the main link between the geometry and the algebra used for our arithmetic applications: the (discrete-time) geodesic ow on quotients of Bruhat{Tits trees by arithmetic lattices.

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Susan E. Swedo,Judith L. RapoportLet K be a (global) function field over F. of genus g, let v be a (normaliseddiscrete) valuation of K, let K. be the associated completion of K, and let R.be the affine function ring associated with v.

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Potentials, Critical Exponents,and Gibbs CocyclesLet X be a geodesically complete proper CAT(–1) space, let x. ∈ X be an arbitrary basepoint, and let Γ be a nonelementary discrete group of isometries of X.

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Symbolic Dynamics of Geodesic Flows on TreesIn this chapter, we give a coding of the discrete-time geodesic ow on the nonwandering sets of quotients of locally finite simplicial trees X without terminal vertices by nonelementary discrete subgroups of Aut(X) by a subshift of finite type on a countable alphabet.

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Random Walks on Weighted Graphs of GroupsLet X be a locally finite simplicial tree without terminal vertices, and let X = ∣X∣.be its geometric realisation. Let Γ be a nonelementary discrete subgroup of Aut(X).

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