arXiv subjects

Yimin Xiao

Publications and source records attributed to Yimin Xiao.

At least 19 recordsLinked to original sources

arXiv2026

Small-time heat decay for stable processes on fractal drums

In this paper, we study the spectral heat content for isotropic stable processes on fractal drums (namely, open sets with fractal boundaries). The spectral heat content for subordinate killed Brownian motions by stable subordinators was investigated in \cite{PX23}, and the present work serves as a natural extension of \cite{PX23} for the spectral heat content for stable processes. Under suitable geometric conditions on the underlying domains, we show that the decay rate of the spectral heat content for stable processes differs substantially from that for subordinate killed Brownian motions when $α=d-\b$, where $\b$ is the interior Minkowski dimension of the boundary of the underlying open set.

math.PR↗

arXiv2026

Strassen's local law of the iterated logarithm for the generalized fractional Brownian motion

Let $X:=\{X(t)\}_{t\ge0}$ be a generalized fractional Brownian motion given by $$ \{X(t)\}_{t\ge0}\overset{d}{=}\left\{ \int_{\mathbb R} \left((t-u)_+^α-(-u)_+^α \right) |u|^{-γ/2} B(du) \right\}_{t\ge0}, $$ with parameters $γ\in (0, 1)$ and $α\in \left(-1/2+ γ/2, \, 1/2+γ/2\right)$. This process was introduced by Pang and Taqqu (2019) as the scaling limit of a class of power-law shot noise processes. The parameters $α$ and $γ$ govern the probabilistic and statistical properties of $X$. In particular, the parameter $γ$ breaks the stationarity of increments of $X$. In this paper, we establish Strassen's local law of the iterated logarithm for $X$ at a given point $t_0 \in (0, \infty)$. This result describes explicitly the roles played by the parameters $α, γ$, and the location $t_0$. Our theorem differs from the earlier Strassen's {global law of the iterated logarithm} for $X$ proved by Ichiba, Pang and Taqqu (2022).

math.PR↗

arXiv2026

Polarity of points for Gaussian random fields in critical dimension

We study the property of hitting points for a class of $\mathbb{R}^d$-valued continuous Gaussian random fields on $\mathbb{R}^N$ with stationary increments, i.i.d. coordinates, and a regularly varying variance function $σ$ of index $0<H<1$. We first prove that if \[ \lim_{r\to 0^+} \frac{r^N}{σ^d\left(r\left( \log\log\frac{1}{r}\right)^{-1/N}\right)} = \infty, \] then every fixed point is polar (i.e., not hit almost surely). In general, this criterion may not be optimal in the critical dimension $d=N/H$. To aim for an optimal condition, we consider the specific case $σ(r) = r^H (\log(1/r))^γ$ and prove that, in the critical dimension $d=N/H$, points are polar if and only if $γ\le 1/d$, or equivalently in this specific case, \[ \int_{0^+} \frac{r^{N-1}}{σ^d(r)} dr = \infty. \] This integral condition is also necessary for points to be polar under general assumptions. Our main contribution lies in the proof of sufficiency of this condition in the specific case, where we extend a covering argument of Talagrand (1998) based on sojourn time estimates to obtain Hausdorff measure bounds and solve polarity of points in the critical dimension.

math.PR↗

arXiv2025

Uniform dimension theorems for parabolic SPDEs

Consider the following $p$-dimensional system of Itô type stochastic PDEs, \begin{align*}\left[\begin{aligned} &\partial_t u(t\,,x) = \partial^2_x u(t\,,x) + b(u(t\,,x)) + σ(u(t\,,x)) ξ(t\,,x)\\ &\text{for $(t\,,x)\in(0\,,\infty)\times\mathbb{T}$, subject to $u(0) \equiv u_0$ on $\mathbb{T}$}, \end{aligned}\right.\end{align*} where $\mathbb{T}$ denotes a given one-dimensional torus, the initial data $u_0:\mathbb{T}\to\mathbb{R}^p$ is assumed to be fixed and non-random and in $C^{1/2}(\mathbb{T}\,;\mathbb{R}^p)$, and $ξ$ denotes a $p$-dimensional space-time white noise. Under certain regularity conditions on $b$ and $σ$, it is proved that, if $p \ge 4$, then \begin{equation*} \mathrm{P}\{\operatorname{dim_{_H}} u(\{t\}\times F) = 2\operatorname{dim_{_H}} F \ \text{$\forall$compact $F\subset\mathbb{T}$, $t>0$}\}=1. \end{equation*} If in addition the matrix $σ(v)$ does not depend on $v\in\mathbb{R}^p$, and is nonsingular, then the above equality holds for all $p\ge2$.

math.PR↗

arXiv2025

Toward Machine Translation Literacy: How Lay Users Perceive and Rely on Imperfect Translations

As Machine Translation (MT) becomes increasingly commonplace, understanding how the general public perceives and relies on imperfect MT is crucial for contextualizing MT research in real-world applications. We present a human study conducted in a public museum (n=452), investigating how fluency and adequacy errors impact bilingual and non-bilingual users' reliance on MT during casual use. Our findings reveal that non-bilingual users often over-rely on MT due to a lack of evaluation strategies and alternatives, while experiencing the impact of errors can prompt users to reassess future reliance. This highlights the need for MT evaluation and NLP explanation techniques to promote not only MT quality, but also MT literacy among its users.

cs.CL↗

arXiv2025

Hitting probabilities, thermal capacity, and Hausdorff dimension results for the Brownian sheet

Let $W= \{W(t): t \in \mathbb{R}_+^N \}$ be an $(N, d)$-Brownian sheet and let $E \subset (0, \infty)^N$ and $F \subset \mathbb{R}^d$ be compact sets. We prove a necessary and sufficient condition for $W(E)$ to intersect $F$ with positive probability and determine the essential supremum of the Hausdorff dimension of the intersection set $W(E)\cap F$ in terms of the thermal capacity of $E \times F$. This extends the previous results of Khoshnevisan and Xiao (2015) for the Brownian motion and Khoshnevisan and Shi (1999) for the Brownian sheet in the special case when $E \subset (0, \infty)^N$ is an interval.

math.PR↗

arXiv2025

Temporal regularity for the stochastic heat equation with rough dependence in space

Consider the nonlinear stochastic heat equation $$ \frac{\partial u (t,x)}{\partial t}=\frac{\partial^2 u (t,x)}{\partial x^2}+ σ(u (t,x))\dot{W}(t,x),\quad t> 0,\, x\in \mathbb{R}, $$ where $\dot W$ is a Gaussian noise which is white in time and has the covariance of a fractional Brownian motion with Hurst parameter $H\in(\frac 14,\frac 12)$ in the space variable. When $σ(0)=0$, the well-posedness of the solution and its Hölder continuity have been proved by Hu et al. \cite{HHLNT2017}. In this paper, we study the asymptotic properties of the temporal gradient $u(t+\varepsilon, x)-u(t, x)$ at any fixed $t \ge 0$ and $x\in \mathbb R$, as $\varepsilon\downarrow 0$. As applications, we deduce Khintchine's law of iterated logarithm, Chung's law of iterated logarithm, and a result on the $q$-variations of the temporal process $\{u(t, x)\}_{t \ge 0}$, where $x\in \mathbb R$ is fixed.

math.PR↗

arXiv2025

The Hidden Language of Harm: Examining the Role of Emojis in Harmful Online Communication and Content Moderation

Social media platforms have become central to modern communication, yet they also harbor offensive content that challenges platform safety and inclusivity. While prior research has primarily focused on textual indicators of offense, the role of emojis, ubiquitous visual elements in online discourse, remains underexplored. Emojis, despite being rarely offensive in isolation, can acquire harmful meanings through symbolic associations, sarcasm, and contextual misuse. In this work, we systematically examine emoji contributions to offensive Twitter messages, analyzing their distribution across offense categories and how users exploit emoji ambiguity. To address this, we propose an LLM-powered, multi-step moderation pipeline that selectively replaces harmful emojis while preserving the tweet's semantic intent. Human evaluations confirm our approach effectively reduces perceived offensiveness without sacrificing meaning. Our analysis also reveals heterogeneous effects across offense types, offering nuanced insights for online communication and emoji moderation.

cs.CL↗

arXiv2025

Sustaining Human Agency, Attending to Its Cost: An Investigation into Generative AI Design for Non-Native Speakers' Language Use

AI systems and tools today can generate human-like expressions on behalf of people. It raises the crucial question about how to sustain human agency in AI-mediated communication. We investigated this question in the context of machine translation (MT) assisted conversations. Our participants included 45 dyads. Each dyad consisted of one new immigrant in the United States, who leveraged MT for English information seeking as a non-native speaker, and one local native speaker, who acted as the information provider. Non-native speakers could influence the English production of their message in one of three ways: labeling the quality of MT outputs, regular post-editing without additional hints, or augmented post-editing with LLM-generated hints. Our data revealed a greater exercise of non-native speakers' agency under the two post-editing conditions. This benefit, however, came at a significant cost to the dyadic-level communication performance. We derived insights for MT and other generative AI design from our findings.

cs.HC↗

arXiv2025

Comparing Native and Non-native English Speakers' Behaviors in Collaborative Writing through Visual Analytics

Understanding collaborative writing dynamics between native speakers (NS) and non-native speakers (NNS) is critical for enhancing collaboration quality and team inclusivity. In this paper, we partnered with communication researchers to develop visual analytics solutions for comparing NS and NNS behaviors in 162 writing sessions across 27 teams. The primary challenges in analyzing writing behaviors are data complexity and the uncertainties introduced by automated methods. In response, we present \textsc{COALA}, a novel visual analytics tool that improves model interpretability by displaying uncertainties in author clusters, generating behavior summaries using large language models, and visualizing writing-related actions at multiple granularities. We validated the effectiveness of \textsc{COALA} through user studies with domain experts (N=2+2) and researchers with relevant experience (N=8). We present the insights discovered by participants using \textsc{COALA}, suggest features for future AI-assisted collaborative writing tools, and discuss the broader implications for analyzing collaborative processes beyond writing.

cs.HC↗

arXiv2025

Local times of anisotropic Gaussian random fields and stochastic heat equation

We study the local times of a large class of Gaussian random fields satisfying strong local nondeterminism with respect to an anisotropic metric. We establish moment estimates and Hölder conditions for the local times of the Gaussian random fields. Our key estimates rely on geometric properties of Voronoi partitions with respect to an anisotropic metric and the use of Besicovitch's covering theorem. As a consequence, we deduce sample path properties of the Gaussian random fields that are related to Chung's law of the iterated logarithm and modulus of non-differentiability. Moreover, we apply our results to systems of stochastic heat equations with additive Gaussian noise and determine the exact Hausdorff measure function with respect to the parabolic metric for the level sets of the solutions.

math.PR↗

arXiv2024

Sample path properties and small ball probabilities for stochastic fractional diffusion equations

We consider the following stochastic space-time fractional diffusion equation with vanishing initial condition:$$ \partial^β u(t, x)=- \left(-Δ\right)^{α/ 2} u(t, x)+ I_{0+}^γ\left[\dot{W}(t, x)\right],\quad t\in[0,T],\: x \in \mathbb{R}^d,$$ where $α>0$, $β\in(0,2)$, $γ\in[0,1)$, $\left(-Δ\right)^{α/2}$ is the fractional/power of Laplacian and $\dot{W}$ is a fractional space-time Gaussian noise. We prove the existence and uniqueness of the solution and then focus on various sample path regularity properties of the solution. More specifically, we establish the exact uniform and local moduli of continuity and Chung-type laws of the iterated logarithm. The small ball probability is also studied.

math.PR↗

arXiv2024

(Dis)placed Contributions: Uncovering Hidden Hurdles to Collaborative Writing Involving Non-Native Speakers, Native Speakers, and AI-Powered Editing Tools

Content creation today often takes place via collaborative writing. A longstanding interest of CSCW research lies in understanding and promoting the coordination between co-writers. However, little attention has been paid to individuals who write in their non-native language and to co-writer groups involving them. We present a mixed-method study that fills the above gap. Our participants included 32 co-writer groups, each consisting of one native speaker (NS) of English and one non-native speaker (NNS) with limited proficiency. They performed collaborative writing adopting two different workflows: half of the groups began with NNSs taking the first editing turn and half had NNSs act after NSs. Our data revealed a "late-mover disadvantage" exclusively experienced by NNSs: an NNS's ideational contributions to the joint document were suppressed when their editing turn was placed after an NS's turn, as opposed to ahead of it. Surprisingly, editing help provided by AI-powered tools did not exempt NNSs from being disadvantaged. Instead, it triggered NSs' overestimation of NNSs' English proficiency and agency displayed in the writing, introducing unintended tensions into the collaboration. These findings shed light on the fair assessment and effective promotion of a co-writer's contributions in language diverse settings. In particular, they underscore the necessity of disentangling contributions made to the ideational, expressional, and lexical aspects of the joint writing.

cs.HC↗

arXiv2024

Phase transition in the EM scheme of an SDE driven by $α$-stable noises with $α\in (0,2]$

We study in this paper the EM scheme for a family of well-posed critical SDEs with the drift $-x\log(1+|x|)$ and $α$-stable noises. Specifically, we find that when the SDE is driven by a rotationally symmetric $α$-stable processes with $α=2$ (i.e. Brownian motion), the EM scheme is bounded in the $L^2$ sense uniformly w.r.t. the time. In contrast, if the SDE is driven by a rotationally symmetric $α$-stable process with $α\in (0,2)$, all the $β$-th moments, with $β\in (0,α)$, of the EM scheme blow up. This demonstrates a phase transition phenomenon as $α\uparrow 2$. We verify our results by simulations.

math.PR↗

arXiv2023

Physician Detection of Clinical Harm in Machine Translation: Quality Estimation Aids in Reliance and Backtranslation Identifies Critical Errors

A major challenge in the practical use of Machine Translation (MT) is that users lack guidance to make informed decisions about when to rely on outputs. Progress in quality estimation research provides techniques to automatically assess MT quality, but these techniques have primarily been evaluated in vitro by comparison against human judgments outside of a specific context of use. This paper evaluates quality estimation feedback in vivo with a human study simulating decision-making in high-stakes medical settings. Using Emergency Department discharge instructions, we study how interventions based on quality estimation versus backtranslation assist physicians in deciding whether to show MT outputs to a patient. We find that quality estimation improves appropriate reliance on MT, but backtranslation helps physicians detect more clinically harmful errors that QE alone often misses.

cs.CL↗

arXiv2023

Approximation of the invariant measure for stable SDE by the Euler-Maruyama scheme with decreasing step-sizes

Let $(X_t)_{t \ge 0}$ be the solution of the stochastic differential equation $$dX_t = b(X_t) dt+A dZ_t, \quad X_{0}=x,$$ where $b: \mathbb{R}^d \rightarrow \mathbb R^d$ is a Lipschitz function, $A \in \mathbb R^{d \times d}$ is a positive definite matrix, $(Z_t)_{t\geq 0}$ is a $d$-dimensional rotationally invariant $α$-stable Lévy process with $α\in (1,2)$ and $x\in\mathbb{R}^{d}$. We use two Euler-Maruyama schemes with decreasing step sizes $Γ= (γ_n)_{n\in \mathbb{N}}$ to approximate the invariant measure of $(X_t)_{t \ge 0}$: one with i.i.d. $α$-stable distributed random variables as its innovations and the other with i.i.d. Pareto distributed random variables as its innovations. We study the convergence rate of these two approximation schemes in the Wasserstein-1 distance. For the first scheme, when the function $b$ is Lipschitz and satisfies a certain dissipation condition, we show that the convergence rate is $γ^{1/α}_n$. Under an additional assumption on the second order directional derivatives of $b$, this convergence rate can be improved to $γ^{1+\frac 1 α-\frac{1}κ}_n$ for any $κ\in [1,α)$. For the second scheme, when the function $b$ is twice continuously differentiable, we obtain a convergence rate of $γ^{\frac{2-α}α}_n$. We show that the rate $γ^{\frac{2-α}α}_n$ is optimal for the one dimensional stable Ornstein-Uhlenbeck process. Our theorems indicate that the recent remarkable result about the unadjusted Langevin algorithm with additive innovations can be extended to the SDEs driven by an $α$-stable Lévy process and the corresponding convergence rate has a similar behaviour. Compared with the previous result, we have relaxed the second order differentiability condition to the Lipschitz condition for the first scheme.

math.PR↗

arXiv2023

An Optimal Uniform Modulus of Continuity for Harmonizable Fractional Stable Motion

Non-Gaussian Harmonizable Fractional Stable Motion (HFSM) is a natural and important extension of the well-known Fractional Brownian Motion to the framework of heavy-tailed stable distributions. It was introduced several decades ago; however its properties are far from being completely understood. In our present paper we determine the optimal power of the logarithmic factor in a uniform modulus of continuity for HFSM, which solves an open old problem. The keystone of our strategy consists in Abel transforms of the LePage series expansions of the random coefficients of the wavelets series representation of HFSM. Our methodology can be extended to more general harmonizable stable processes and fields.

math.PR↗

arXiv2023

Polarity of points for systems of nonlinear stochastic heat equations in the critical dimension

Let $u(t, x) = (u_1(t, x), \dots, u_d(t, x))$ be the solution to the systems of nonlinear stochastic heat equations \[ \begin{split} \frac{\partial}{\partial t} u(t, x) &= \frac{\partial^2}{\partial x^2} u(t, x) + σ(u(t, x)) \dot{W}(t, x),\\ u(0, x) &= u_0(x), \end{split} \] where $t \ge 0$, $x \in \mathbb{R}$, $\dot{W}(t, x) = (\dot{W}_1(t, x), \dots, \dot{W}_d(t, x))$ is a vector of $d$ independent space-time white noises, and $σ: \mathbb{R}^d \to \mathbb{R}^{d\times d}$ is a matrix-valued function. We say that a subset $S$ of $\mathbb{R}^d$ is polar for $\{u(t, x), t \ge 0, x \in \mathbb{R}\}$ if \[ \mathbb{P}\{u(t,x) \in S \text{ for some } t>0 \text{ and } x\in\mathbb{R} \}=0. \] The main result of this paper shows that, in the critical dimension $d=6$, all points in $\mathbb{R}^d$ are polar for $\{u(t, x), t \ge 0, x \in \mathbb{R}\}$. This solves an open problem of Dalang, Khoshnevisan and Nualart (2009, 2013) and Dalang, Mueller and Xiao (2021). We also provide a sufficient condition for a subset $S$ of $\mathbb{R}^d$ to be polar.

math.PR↗