arXiv subjects

Yuanzheng Wang

Publications and source records attributed to Yuanzheng Wang.

4 recordsLinked to original sources

arXiv2026

Directed distances in spanning-tree-decorated planar maps: exact exponent, scaling limit and universality

We define a natural orientation on a spanning-tree-decorated planar map whereby, roughly speaking, each directed edge in the map is oriented to match the direction of the contour exploration of the spanning tree. We study directed distances (lengths of shortest directed paths) with respect to this orientation. We construct the Busemann function which measures directed distances to $\infty$ along a natural interface in the uniform infinite spanning-tree-decorated map. We show that this Busemann function, re-scaled appropriately, converges in law to a $3/2$-stable Lévy process. We also show that in a uniform spanning-tree-decorated map with $n$ edges, directed distances are typically of order $n^{1/3}$. Using a strong coupling argument, we deduce analogous statements for directed distances in other random planar maps in the $\sqrt 2$-Liouville quantum gravity (LQG) universality class, including uniform meandric systems and mated-CRT maps for $γ=\sqrt 2$. These results give the scaling dimension for a hypothetical directed version of the $\sqrt 2$-LQG metric. Our proof strategy is inspired by work of Borga and Gwynne (2025) on directed distances in bipolar-oriented triangulations.

math.PR↗

arXiv2026

StrategyBench: Evaluating Explicit Strategy Induction in Large Language Models

As large language models are increasingly used in data-scarce and evolving task scenarios, few-shot in-context learning (ICL) has become a key paradigm for task adaptation. However, direct ICL often uses a small set of examples without explicitly abstracting task rules, making it sensitive to example construction. In contrast, human learners often reduce such sensitivity by first summarizing task rules from examples and then applying them to new instances. To evaluate this ability, we propose StrategyBench, which selects strategy-inducible tasks from BIG-Bench, constructs reference strategies, and defines evaluation metrics along two dimensions: strategy quality and downstream utility. We further analyze strategy induction from three perspectives: task variation, model configuration, and adaptation setting, covering category-wise differences, generator-executor choices, demonstration design, and SFT-based adaptation. Experiments show that explicit strategy utility differs substantially across task categories and depends on both strategy generation and execution conditions. The benchmark is released at: https://anonymous.4open.science/r/StrategyBench-D53C.

cs.AI↗

arXiv2025

Efficiently matching random inhomogeneous graphs via degree profiles

In this paper, we study the problem of recovering the latent vertex correspondence between two correlated random graphs with vastly inhomogeneous and unknown edge probabilities between different pairs of vertices. Inspired by and extending the matching algorithm via degree profiles by Ding, Ma, Wu and Xu (2021), we obtain an efficient matching algorithm as long as the minimal average degree is at least $Ω(\log^{2} n)$ and the minimal correlation is at least $1 - O(\log^{-2} n)$.

cs.DS↗

arXiv2024

Sharp asymptotics of disconnection time of large cylinders by simple and biased random walks

We investigate the asymptotic disconnection time of a large discrete cylinder $(\mathbb{Z}/N\mathbb{Z})^{d}\times \mathbb{Z}$, $d\geq 2$, by simple and biased random walks. For simple random walk, we derive a sharp asymptotic lower bound that matches the upper bound from [Sznitman, Ann. Probab., 2009]. For biased walks, we obtain bounds that asymptotically match in the principal order when the bias is not too strong, which greatly improves non-matching bounds from [Windisch, Ann. Appl. Probab., 2008]. As a crucial tool in the proof, we also obtain a "very strong" coupling between the trace of random walk on the cylinder and random interlacements, which is of independent interest.

math.PR↗