Probability on Trees and Networks

By Russell Lyons, Yuval Peres. 2017

895 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/406abd37c8fdde8b42286113edee45165b711c26

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In Geometry and Topology

In Mathematical Physics

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Citations in the corpus

Walking in the Shadow: A New Perspective on Descent Directions for Constrained Minimization (2020, background): “Smooth convex optimization problems over polytopes are an important class of problems that appear in many settings, such as low-rank matrix completion [1], structured supervised learning [2, 3], electrical flows over graphs [4], video co-localization in computer vision [5], traffic assignment proble”
Branching random walks (2015, background): “In the literature, a property is called inherited (Peres [208] Chapter 3, Lyons and Peres [178] Chapter 5), if it is satisfied by all finite trees and is such that whenever a tree has this property, so do all the subtrees rooted at the children of the root.”
Random Walks and Heat Kernels on Graphs (2017, background): “This concept is well documented in the literature, and we will not elaborate it here; see [1,6,10] for good expositions on electric networks and effective resistance.”
Recurrence versus transience for weight-dependent random connection models (2019, neutral): “We restrict ourselves to recalling some basic results that we need in our proofs, a comprehensive treatment of the theory can be found for instance in [26].”
Hyperbolic and Parabolic Unimodular Random Maps (2016, background): “s Br(M;Xnm) yield an innite collection of disjoint cutsets of degree sum at most Dseparating ˆfrom innity in the subgraph induced by Wi. Thus, this graph is recurrent by the Nash-Williams criterion [60], a contradiction. 7.2Theorem 1in the multiply-connected planar case In light ofTheorem 7.1we need”
Speed of random walks, isoperimetry and compression of finitely generated groups (2015, methodology): “in Linial-Magen [LM00], Newman-Rabinovich [NR03] and was extended in Grigorchuk-Nowak [GN12], JolissaintValette [JV14] and Mimura [Mim15]. Interested readers may also consult Chapter 13.5 in the book [LP16] for a nice introduction to this topic. Let (M,dM) be a ﬁnite metric space, K: M × M → [0,1] a”