Spin systems with hyperbolic symmetry: a survey Article Swipe
Related Concepts
Probabilistic logic
Symmetry (geometry)
Spin (aerodynamics)
Random walk
Statistical physics
Theoretical physics
Physics
Mathematics
Statistics
Geometry
Thermodynamics
Roland Bauerschmidt
,
Tyler Helmuth
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2109.02566
· OA: W4389787705
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2109.02566
· OA: W4389787705
Spin systems with hyperbolic symmetry originated as simplified models for the Anderson metal--insulator transition, and were subsequently found to exactly describe probabilistic models of linearly reinforced walks and random forests. In this survey we introduce these models, discuss their origins and main features, some existing tools available for their study, recent probabilistic results, and relations to other well-studied probabilistic models. Along the way we discuss some of the (many) open questions that remain.
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