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math.PR2020
Limit theorems for topological invariants of the dynamic multi-parameter simplicial complex
Takashi Owada, Gennady Samorodnitsky, Gugan Thoppe
Topological study of existing random simplicial complexes is non-trivial and has led to several seminal works. However, the applicability of such studies is limited since the rando…
math.PR2018
Betti Numbers of Gaussian Excursions in the Sparse Regime
Gugan Thoppe, Sunder Ram Krishnan
Random field excursions is an increasingly vital topic within data analysis in medicine, cosmology, materials science, etc. This work is the first detailed study of their Betti num…