arXiv subjects

Zelin Lv

Publications and source records attributed to Zelin Lv.

5 recordsLinked to original sources

arXiv2026

The Sixth Moment of Random Determinants for Arbitrarily Distributed Random Entries

Via the method of marked permutation tables presented in this paper, we generalize the formula for the sixth moment of a random determinant to account for entries with arbitrary distribution. That is, let $f_6(n) = \mathbb{E}(\det A)^6$, where $A$ is an $n$ by $n$ random matrix with independent and identically distributed entries. We show that the exponential generating function $F_6(t) = \sum_{n=0}^\infty f_6(n)t^n/(n!)^2$ is D-finite and we present it in a closed form. Our method relies on carefully decomposing marked permutation tables into a shell, a core, and a floating component, each of which has a separate contribution to $F_6(t)$. After this decomposition, it is sufficient to enumerate over a finite number of possible shells, which we did using a highly intricate computer program. We verified our result up to $n = 7$ in the general case and up to $n = 9$ for random matrices whose entries only take two values by using a different method for computing $f_6(n)$ for these cases.

math.CO↗

arXiv2026

LabRobFail: A Benchmark for Robotic Failure Analysis in Chemical Self-driving Laboratory

The deployment of embodied agents in self-driving laboratories could accelerate scientific discovery, yet their reliability is constrained by the irreversible and safety-critical nature of chemical experiments. Progress is further hindered by scarce failure data and the lack of fine-grained evaluation protocols. To address these challenges, we introduce LabRobFail, a failure-centric framework for learning and evaluating robotic failure analysis in chemical laboratories. LabRobFail-Sim injects controllable failures at the control, physics, and semantic levels, enabling the construction of LabRobFail-Data, which contains over 20,000 trajectories across 70+ task scenarios, five failure categories, and 11 fine-grained failure types. LabRobFail-Bench evaluates six capabilities spanning task understanding, failure detection, temporal localization, severity assessment, failure classification, and actionable correction. We further develop LabRobFail-VLM, a domain-specialized vision-language model that generates structured failure diagnoses and recovery instructions. On seen environments, it achieves 90.83% failure-detection accuracy and 77.21% temporal-localization accuracy, substantially outperforming general-purpose VLMs. When integrated as a real-time supervisor, it improves downstream task success rates by 4-16 percentage points, demonstrating the value of fine-grained failure understanding for closed-loop recovery and reliable laboratory autonomy. Our code and data are available at https://github.com/Su-ISE-2001/SciRobo

cs.RO↗

arXiv2025

Analysing the Moments of the Determinant of a Random Matrix Via Analytic Combinatorics of Permutation Tables

We consider the following natural question. Given a matrix $A$ with i.i.d. random entries, what are the moments of the determinant of $A$? In other words, what is $\mathbb{E}[\det(A)^k]$? While there is a general expression for $\mathbb{E}[\det(A)^k]$ when the entries of $A$ are Gaussian, much less is known when the entries of $A$ have some other distribution. In two recent papers, we answered this question for $k = 4$ when the entries of $A$ are drawn from an arbitrary distribution and for $k = 6$ when the entries of $A$ are drawn from a distribution which has mean $0$. These analyses used recurrence relations and were highly intricate. In this paper, we show how these analyses can be simplified considerably by using analytic combinatorics on permutation tables.

math.CO↗

arXiv2024

On the second moment of the determinant of random symmetric, Wigner, and Hermitian matrices

In this paper, we analyze the second moment of the determinant of random symmetric, Wigner, and Hermitian matrices. Using analytic combinatorics techniques, we determine the second moment of the determinant of Hermitian matrices whose entries on the diagonal are i.i.d and whose entries above the diagonal are i.i.d. and have real expected values. Our results extend previous work analyzing the second moment of the determinant of symmetric and Wigner matrices, providing a unified approach for this analysis.

math.CO↗

arXiv2023

The Sixth Moment of Random Determinants

In this paper, we determine the sixth moment of the determinant of an asymmetric $n \times n$ random matrix where the entries are drawn independently from an arbitrary distribution $Ω$ with mean $0$. Furthermore, we derive the asymptotic behavior of the sixth moment of the determinant as the size of the matrix tends to infinity.

math.CO↗