Point processes, cost, and the growth of rank in locally compact groups

DOI10.1007/s11856-022-2445-9OpenAlexW4287328219MaRDI QIDQ2689226

Sam Mellick, Miklós Abért

Publication date: 9 March 2023

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.07710

Mathematics Subject Classification ID

Ergodic theory (37Axx) Stochastic processes (60Gxx) Measure-theoretic ergodic theory (28Dxx)

Related Items (1)

Isomorphisms of Poisson systems over locally compact groups

Cites Work

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• Metric geometry of locally compact groups
• Poisson thickening
• Poisson splitting by factors
• Rank gradient, cost of groups and the rank versus Heegaard genus problem
• Invariant Palm and related disintegrations via skew factorization
• Poisson process Fock space representation, chaos expansion and covariance inequalities
• Entropy and isomorphism theorems for actions of amenable groups
• Borel chromatic numbers
• Von Neumann's problem and extensions of non-amenable equivalence relations
• Rank, combinatorial cost, and homology torsion growth in higher rank lattices
• Trees and matchings from point processes
• Tree and grid factors for general point processes
• On the virtual groups defined by ergodic actions of R\(^n\) and \(Z^n\)
• \(\ell^2\) invariants of equivalence relations and groups
• Topics in orbit equivalence
• Invariant proper metrics on coset spaces
• Cost of equivalence relations and groups
• On the asymptotic number of generators of high rank arithmetic lattices
• Growth of mod-2 homology in higher-rank locally symmetric spaces
• Finitary isomorphisms of Poisson point processes
• On the growth of \(L^2\)-invariants for sequences of lattices in Lie groups
• Palm pairs and the general mass-transport principle
• Heegaard splittings, the virtually Haken conjecture and property \((\tau)\)
• Extra heads and invariant allocations
• Asymptotic invariants of lattices in locally compact groups
• Probability on Trees and Networks
• A survey of Measured Group Theory
• Random Measures, Theory and Applications
• Volume versus rank of lattices
• Simple groups without lattices
• Cut sets and normed cohomology with applications to percolation
• Ergodic decomposition of quasi-invariant probability measures
• COUNTABLE BOREL EQUIVALENCE RELATIONS
• Lebesgue orbit equivalence of multidimensional Borel flows: A picturebook of tilings
• Spectral and mixing properties of actions of amenable groups
• An Introduction to the Theory of Point Processes
• Continuum Percolation
• The 2D‐directed spanning forest is almost surely a tree
• Rank and genus of 3-manifolds
• Bernoulli actions are weakly contained in any free action
• Weak containment of measure-preserving group actions
• All properly ergodic Markov chains over a free group are orbit equivalent
• 𝐿²-Betti numbers of locally compact groups and their cross section equivalence relations
• Lectures on the Poisson Process
• An Introduction to the Theory of Point Processes

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