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SUMMARY:Shu Kanazawa (Kyoto University)
DTSTART:20200821T050000Z
DTEND:20200821T060000Z
DTSTAMP:20260423T004038Z
UID:APATG/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/APATG/3/">La
 w of large numbers for Betti numbers of homogeneous and spatially independ
 ent random simplicial complexes</a>\nby Shu Kanazawa (Kyoto University) as
  part of Asia Pacific Seminar on Applied Topology and Geometry\n\n\nAbstra
 ct\nThe Erdős–Rényi graph model has been extensively studied since the
  1960s as a typical random graph model. Recently\, the study of random sim
 plicial complexes has drawn attention as a higher-dimensional generalizati
 on of random graphs. In this talk we introduce a class of homogeneous and 
 spatially independent random simplicial complexes\, and discuss the asympt
 otic behavior of their Betti numbers. This result extends the law of large
  numbers for Betti numbers of Linial–Meshulam complexes\, obtained in an
  earlier study by Linial and Peled. Time permitting\, we will also discuss
  the convergence of the empirical spectral distributions of their Laplacia
 ns. A key element in the argument is the local weak convergence of simplic
 ial complexes. Inspired by the work of Linial and Peled\, we establish the
  local weak limit theorem for homogeneous and spatially independent random
  simplicial complexes.\n
LOCATION:https://researchseminars.org/talk/APATG/3/
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