Author

V. Koval

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Preprint Aug 2026

Peripheral Traps and Lower Bounds on Mixing Times for Random Walks on Sparse Heavy-Tailed Random Intersection Graphs

This paper analyzes mixing time lower bounds for random walks on sparse, heavy-tailed Random Intersection Graphs. In sparse feature regimes, heavy-tailed feature distributions lead to the formation of peripheral trap -- chains of overlapping low-weight feature cliques attached to high-weight hub nodes within the graph's giant component. By modeling escape trajectories from these traps as continuous limit hitting times for reflected Brownian motion, the analysis demonstrates that random walks experience logarithmic squared delays. Consequently, the mixing time is bounded below by $\Omega(\log^2 n)$, and the local total variation distance exhibits non-concentrated decay, formally preventing a sharp cutoff phenomenon.

V. Koval · 0 citations

Preprint Jul 2026

Meeting and coalescence times for random walks in the largest component of the Erd\H{o}s-R\'enyi random graph

We prove that the stationary and worst-case expected meeting times of two independent continuous-time random walks on the largest component of the Erd\H{o}s-R\'enyi random graph $G(n,p)$ have order $n$ throughout the strictly supercritical, the slightly supercritical and the critical regimes. Using these bounds along with a fine-tuned combination of comparison inequalities due to Oliveira (2012) and Kanade-Mallmann-Trenn-Sauerwald (KMS, 2023), we deduce that expected coalescence time and full voter-model consensus also have order $n$ throughout these three regimes.

V. Koval, Y. Peres, Pieter Trapman · 1 citation