Papers › Minimum stationary values of sparse random directed graphs
Minimum stationary values of sparse random directed graphs
Xing Shi Cai, Guillem Perarnau
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We consider the stationary distribution of the simple random walk on the directed configuration model with bounded degrees. Provided that the minimum out-degree is at least $2$, with high probability (whp) there is a unique stationary distribution. We show that the minimum positive stationary value is whp n^(-(1+C+o(1))) for some constant C ≥0 determined by the degree distribution. In particular, C is the competing combination of two factors: (1) the contribution of atypically "thin" in-neighbourhoods, controlled by subcritical branching processes; and (2) the contribution of atypically "light" trajectories, controlled by large deviation rate functions. Additionally, our proof implies that whp the hitting and the cover time are both n^(1+C+o(1)). Our results complement those of Caputo and Quattropani who showed that if the minimum in-degree is at least 2, stationary values have logarithmic fluctuations around n⁻¹.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections