Author

Run-Sheng Liu

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Preprint Nov 2026

Local scaling limit of the four-dimensional uniform spanning tree

In this paper, we prove that the uniform spanning tree of $\mathbb Z^4$, seen from the origin, converges locally to an infinite spatial Brownian Kesten tree: a Brownian spine onto which independent spatial Brownian trees are grafted at a constant rate. The convergence holds jointly for the intrinsic metric, the volume...

Run-Sheng Liu · 0 citations

2026

A Cyclic Vernier Time-to-Digital Converter With Tunable Time Amplification for Endpoint Clock-to-Data Interval Measurement in FPGAs

Quantitative reconstruction of endpoint-local clock-to-data intervals during operation can complement static timing analysis (STA) when local process, voltage, and temperature (PVT) variation, supply disturbances, and aging shift setup margin. Existing in situ monitors are commonly either error-triggered, which require...

Song-Xuan He, Wang-Yong Chen, Run-Sheng Liu et al. · IEEE Transactions on Instrum... · 0 citations

Preprint Sep 2026

Intersection Exponents of Simple Random Walks in Two and Three Dimensions

The probability that several independent random walks avoid one another decays algebraically with the number of steps $N\to\infty$ in two and three dimensions, $P_N\sim N^{-\xi/2}$, where the intersection exponent $\xi$ depends on the number of random walks. More generally, one may consider several groups of independen...

Qi-Yuan Shi, Run-Sheng Liu, Xin-Yi Li et al. · 0 citations