Random walk in random groups

By Misha Gromov. 2003

526 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6fc962010e1e3be68f6c327f0cd55b56e545a0ad

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The Baum-Connes and the Farrell-Jones Conjectures in K- and L-Theory (2004, background): “Recent work of Farrell–Jones (see [114–116] and [161]) makes use of a variant of the Cheeger–Fukaya-Gromov collapsing theory.”
Expander graphs in pure and applied mathematics (2011, unknown): “eir way into the main chapters. (I) The Baum-Connes conjecture: This is a famous deep conjecture. For a user-friendly introduction see [Va3]. Counterexamples to a generalized form of it were given in [Gro1] and [HLS]. The original conjecture is still open though it was proved for many classes of gro”
Poincaré inequalities, embeddings, and wild groups (2010, methodology): “It was shown in [14, 32, 3] that for every d > 2, for large enough j (depending only on d and the parameters k, η), the group Γ(Gn, d, j) is torsion-free and hyperbolic with probability tending to 1 as n→∞.”
The ideal structure of reduced crossed products (2008, background): “A counterexample needs an improvement of Gromov’s construction in [9].”
Combinatorial Harmonic Maps and Discrete-group Actions on Hadamard Spaces (2004, background): “This provides a negative answer to the question asked by Gromov in [10].”
Entropy and isoperimetry for linear and non-linear group actions (2008, background): “(a) Random quotients of all resilient groups (see [15]), e.”
Isometric Group Actions on Hilbert Spaces: Growth of Cocycles (2005, background): “nt with respect to the corresponding aﬃne action on H π. By an unpublished result of Shalom (for a proof, see Corollary 3.3.10 in [BHV]), the map F is harmonic. We may now appeal to Gromov’s results ([Gro2], section 3.7.D’; see also Proposition 3.3.21 in [BHV]) on the growth of harmonic, equivariant”