Stable random fields, Patterson-Sullivan measures and extremal cocycle growth
DOI10.1007/s00440-022-01134-zOpenAlexW2956041354MaRDI QIDQ2159250
Parthanil Roy, Jayadev S. Athreya, Mahan Mitra
Publication date: 28 July 2022
Published in: Probability Theory and Related Fields (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1809.08295
Teichmüller spacegeodesic flowPatterson-Sullivan measureextreme value theorystable random fieldergodicity and mixingCAT(-1) spacehigher rank symmetric spaceBowen-Margulis measureRosiński representation
Geometric group theory (20F65) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Fractals (28A80) Asymptotic properties of groups (20F69) Hyperbolic groups and nonpositively curved groups (20F67) Boundary theory for Markov processes (60J50) Hausdorff and packing measures (28A78) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Ergodic theory (37Axx)
Cites Work
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- Lattice point asymptotics and volume growth on Teichmüller space
- The asymptotic distribution of circles in the orbits of Kleinian groups
- Generalized conformal densities for higher products of rank one Hadamard spaces.
- Normalizer, divergence type, and Patterson measure for discrete groups of the Gromov hyperbolic space
- Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups
- Cannon-Thurston maps for trees of hyperbolic metric spaces
- The density at infinity of a discrete group of hyperbolic motions
- Gauss measures for transformations on the space of interval exchange maps
- Interval exchange transformations and measured foliations
- Hausdorff dimension of sets of nonergodic measured foliations
- The limit set of a Fuchsian group
- Patterson-Sullivan theory in higher rank symmetric spaces
- Mixing, counting, and equidistribution in Lie groups
- Patterson-Sullivan measures on the boundary of a hyperbolic space in the sense of Gromov
- On uniqueness of the spectral representation of stable processes
- Cannon-Thurston maps for hyperbolic group extensions
- Maxima of stable random fields, nonsingular actions and finitely generated abelian groups: a survey
- Growth gap in hyperbolic groups and amenability
- Stable random fields indexed by finitely generated free groups
- Logarithm laws for flows on homogeneous spaces
- Decomposition of stationary \(\alpha\)-stable random fields.
- Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes.
- On the structure of stationary stable processes
- Equidistribution and counting of orbit points for discrete rank one isometry groups of Hadamard spaces
- Harmonicity of quasiconformal measures and Poisson boundaries of hyperbolic spaces
- Stationary symmetric \(\alpha\)-stable discrete parameter random fields
- The ergodic theory of hyperbolic groups
- Skinning measures in negative curvature and equidistribution of equidistant submanifolds
- Flat strips, Bowen–Margulis measures, and mixing of the geodesic flow for rank one CAT(0) spaces
- The Patterson–Sullivan measure and proper conjugation for Kleinian groups of divergence type
- Riemann Surfacese and Related Topics (AM-97)
- Ergodicité et équidistribution en courbure négative
- Equidistribution and counting for orbits of geometrically finite hyperbolic groups
- Statistics and compression of scl
- Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees
- Harmonic measures versus quasiconformal measures for hyperbolic groups