Author

A. Kumar

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Preprint Aug 2026

A multiscale front-decoupling criterion for threshold cascades on unimodular random trees

This is the third paper in a series on threshold cascades of coupled Ornstein-Uhlenbeck diffusions on graphs converging Benjamini-Schramm to a unimodular Galton-Watson tree. In arXiv:2608.15987 the reduction of the cascade to a finite-type Galton-Watson process (front decoupling) was proved unconditionally in the dissi...

A. Kumar, Abhinav Duddala · 0 citations

Preprint Aug 2026

Threshold cascades of interacting diffusions on unimodular random trees: a conditional branching-process universality theorem, the annealed pressure, and the dimension of the failed boundary

We study systems of coupled Ornstein-Uhlenbeck diffusions with an absorbing failure state on finite graphs that converge locally weakly to a unimodular Galton-Watson tree. A single failure can trigger a cascade of threshold crossings, and the central question is when the cascade is subcritical or supercritical and what...

A. Kumar · 2 citations · ⚡1

Preprint Aug 2026

Two problems for threshold cascades of interacting diffusions on unimodular random trees: front propagation with a Bramson correction, and the continuous-type limit theory

Companion to arXiv:2608.XXXXX, which reduces threshold cascades of coupled Ornstein-Uhlenbeck diffusions on graphs converging Benjamini-Schramm to a unimodular Galton-Watson tree, unconditionally in a dissipative regime, to a finite-type Galton-Watson process. Two problems are left open there; we formulate both precise...

A. Kumar, Abhinav Duddala · 1 citation