arXiv subjects

Beatriz Navarro Lameda

Publications and source records attributed to Beatriz Navarro Lameda.

4 recordsLinked to original sources

arXiv2026

Generative AI performance in core undergraduate mathematics: a curriculum-level case study

Generative artificial intelligence (GenAI) tools such as OpenAI's ChatGPT are transforming the educational landscape, prompting reconsideration of traditional assessment practices. In parallel, universities are exploring alternatives to in-person, closed-book examinations, raising concerns about academic integrity and pedagogical alignment in uninvigilated settings. This study systematically investigates the performance of GenAI on typical mathematics questions from across a first-year mathematics curriculum. Adopting an empirical approach and utilising current examination questions as a proxy for course content, we generate, transcribe, and blind-mark GenAI submissions to eight undergraduate mathematics assessments, spanning the entirety of the first-year curriculum. By combining independent GenAI responses to individual questions, we enable a meaningful evaluation of GenAI performance, both at the level of modules and across the first-year curriculum. We find that GenAI attainment is at the level of a first-class degree, though current performance can vary between modules. Further, we find that GenAI performance is remarkably consistent when viewed across the entire curriculum, significantly more so than that of students in invigilated examinations. Our findings evidence the pressing need for redesigning assessments in mathematics in the era of generative artificial intelligence.

cs.CY↗

arXiv2026

On global solutions to the semidiscrete stochastic heat equation

We consider the stochastic heat equation on the integer lattice $\mathbb{Z}^d$ in dimension $d \geq 3$ and with small coupling constant. We show uniqueness of global solutions within the class of positive functions that are stationary in time and whose asymptotic growth in space is subexponential. Our proof relies on a factorization formula for the point-to-point partition function in the associated polymer model.

math.PR↗

arXiv2026

A factorization formula for the partition function in the semi-discrete parabolic Anderson model

We consider a continuous-time simple symmetric random walk on the integer lattice $\mathbb{Z}^d$ in dimension $d \geq 3$, subject to a random potential given by a field of two-sided Wiener processes. In the high-temperature regime, we prove the existence of the $L^2$- and almost sure limits of the partition function as time $t \to \pm \infty$, and show that these limiting partition functions are positive almost surely. Our main result is a factorization formula for the point-to-point partition function, which is shown to be valid up to any sub-ballistic scale.

math.PR↗

arXiv2021

On a factorization formula for the partition function of directed polymers

We prove a factorization formula for the point-to-point partition function associated with a model of directed polymers on the space-time lattice $\mathbb{Z}^{d+1}$, subject to an i.i.d. random potential and in the regime of weak disorder. In particular, we show that the error term in the factorization formula is uniformly small for starting and end points $x, y$ in the sub-ballistic regime $\| x - y \| \leq t^σ$, where $σ< 1$ can be arbitrarily close to $1$. This extends a result of Sinai. We also derive asymptotics for spatial and temporal correlations of the field of limiting partition functions.

math.PR↗