Randomly colored graphs show two regimes: subgraph sizes concentrate when the normalized degree norm ζ is o(1), but monochromatic edges may deviate from their mean with positive probability when ζ is Θ(1) and color imbalance persists.
Kallenberg,Foundations of Modern Probability, Springer-Verlag, New York
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A self-normalized functional limit theorem is proved for linear processes with random coefficients and heavy-tailed innovations, with convergence in the Skorokhod M2 topology on cadlag functions under a bounded partial-sum condition on the coefficients.
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A universal dichotomy for concentration in randomly colored graphs
Randomly colored graphs show two regimes: subgraph sizes concentrate when the normalized degree norm ζ is o(1), but monochromatic edges may deviate from their mean with positive probability when ζ is Θ(1) and color imbalance persists.
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A functional limit theorem for self-normalized linear processes with random coefficients and i.i.d. heavy-tailed innovations
A self-normalized functional limit theorem is proved for linear processes with random coefficients and heavy-tailed innovations, with convergence in the Skorokhod M2 topology on cadlag functions under a bounded partial-sum condition on the coefficients.