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Xinxin Chen

Publications and source records attributed to Xinxin Chen.

At least 19 recordsLinked to original sources
arXiv2026

Fluctuations of additive martingale limits of branching Brownian motion

Consider a one-dimensional branching Brownian motion. Let $W_\infty(\beta)$ denote the limit of the additive martingale in the subcritical regime $\lvert \beta\rvert < \beta_c$ and $Z_\infty$ be the limit of the derivative martingale at criticality. Madaule (Stochastic Process. Appl. 126 (2016), no. 2, 470--502) established the following convergence \[ \frac{W_\infty(\beta)}{\beta_c-\beta}\xrightarrow[\beta\nearrow \beta_c]{\mathbb{P}} 2Z_\infty. \] The goal of this paper is twofold: firstly, we strengthen this result into an almost sure convergence; secondly, we describe the fluctuations occurring in this convergence by proving \[ \frac{1}{\beta_c-\beta}\left( \frac{W_\infty(\beta)}{\beta_c-\beta} - 2 Z_\infty +2(\beta_c-\beta)\log(\beta_c-\beta) Z_\infty\right) \xrightarrow[\beta\nearrow \beta_c]{(d)} S, \] where, conditionally on $Z_\infty$, $S$ follows a spectrally negative 1-stable distribution with scale and shift parameters proportional to $Z_\infty$. Furthermore, these results are extended to the setting of complex additive martingales and the fluctuations to a multi-dimensional convergence.

math.PR↗
arXiv2026

Locally finite fixed points of branching Brownian motion

We give a full characterization of the fixed points of Branching Brownian motion with critical and supercritical drifts under no additional assumptions besides it being locally finite almost surely. In particular, we do not assume finite intensity (Kabluchko, 2012) or the finite top particle (Chen-Garban-Shekhar, 2023) conditions. We also give a full characterization of the domain of attraction of the fixed points of BBM.

math.PR↗
arXiv2026

Branching random walk in random environment

We consider a branching random walk on \(\Z^d\) in a random environment given by Bernoulli site percolation with parameter \(p\in (0,1)\). In this model, each particle located at an open site reproduces according to a law \(\mu_\circ\), whereas a particle at a closed site reproduces according to another law \(\mu_\bullet\). Each newly born child performs an independent simple random walk jump from the position of its parent. We study the quenched survival probability under various assumptions on \((\mu_\circ, \mu_\bullet)\) and establish a Yaglom theorem when both offspring distributions are critical.

math.PR↗
arXiv2026

ProWAFT: A ROMA-LPD Instance for Workload-Aware and Dynamic Fault Tolerance in FPGA-Based CNN Accelerators

SRAM-based FPGAs provide an attractive platform for energy- and latency-constrained CNN inference at the network edge, yet transient faults can lead to silent errors that compromise reliability. Always-on redundancy (e.g., full TMR) improves correctness but incurs substantial performance and energy overhead, while reactive recovery may introduce unacceptable latency on the critical path. We propose \textbf{ProWAFT}, a proactive workload-aware fault-tolerance framework for FPGA-based CNN accelerators that uses partial reconfiguration to selectively apply TMR across reconfigurable partitions. ProWAFT quantifies workload criticality, models fault propagation and reconfiguration overhead, and selects configurations that minimize a composite objective over latency, energy, and reliability risk. Implemented on a Xilinx Zynq UltraScale+ ZCU104 platform with six reconfigurable regions and evaluated on a 500-task trace derived from ResNet-18, MobileNetV2, and EfficientNet-Lite under time-varying SEU injection, ProWAFT achieves lower composite cost than static TMR and reactive reconfiguration while maintaining high task success rate and near-baseline throughput with low online decision overhead.

cs.CL↗
arXiv2026

DAIN: Dynamic Agent-Based Interaction Network for Efficient and Collaborative Multimodal Reasoning

Current multimodal fusion approaches, particularly those based on static Mixture-of-Experts (MoE) architectures, often struggle to provide the adaptive and efficient collaborative reasoning required by complex real-world applications. We introduce the Dynamic Agent-based Interaction Network (DAIN), which reconceptualizes multimodal fusion as a dynamic, multi-agent collaborative process. DAIN employs a context-aware Meta-Controller that dynamically schedules sparse activation of specialized interaction agents and orchestrates compressed inter-agent communication for consensus-building. The framework is guided by a multi-objective loss function that jointly optimizes task accuracy, agent specialization, and operational efficiency through sparse activation and communication regularization. Comprehensive evaluations across five diverse benchmarks -- ADNI, MIMIC-IV, MM-IMDB, CMU-MOSI, and ENRICO -- establish DAIN as a new state-of-the-art, delivering significant performance improvements including a 2.6\% accuracy gain on ADNI. Ablation studies verify the critical roles of both dynamic scheduling and agent communication. Furthermore, DAIN offers enhanced interpretability by exposing context-dependent agent roles and collaboration patterns while maintaining computational efficiency through sample-wise sparse agent activation. Our work demonstrates the promise of dynamic, agent-based paradigms for multimodal reasoning.

cs.CL↗
arXiv2026

Atypical Decay Rates for Atypical Heights in Random Recursive Trees

We establish the large deviation probabilities for the height of random recursive trees, revealing polynomial upper-tail decay and stretched-exponential lower-tail decay. Remarkably, the lower tail features an atypical prefactor that grows to infinity more slowly than any $n$-fold iterated logarithm.

math.PR↗
arXiv2026

Minimum and extremal process for a branching random walk outside the boundary case

This work extends the studies on the minimum and extremal process of a supercritical branching random walk outside the boundary case which cannot be reduced to the boundary case. We study here the situation where the log-generating function explodes at $1$ and the random walk associated to the spine possesses a stretched exponential tail with exponent $b\in(0,\frac12)$. Under suitable conditions, we confirm the conjecture of Barral, Hu and Madaule [Bernoulli 24(2) 2018 801-841], and obtain the weak convergence for the minimum and the extremal process. We also establish an a.s. infimum result over all infinity rays of this system.

math.PR↗
arXiv2025

Yaglom theorem for critical branching random walk on $\mathbb{Z}^d$

We study the critical branching random walk on $\mathbb{Z}^d$ started from a distant point $x$ and conditioned to hit some compact set $K$ in $\mathbb{Z}^d$. We are interested in the occupation time in $K$ and present its asymptotic behaviors in different dimensions. It is shown in this work that the occupation time is of order $\|x\|^{4-d}$ in dimensions $d\leq 3$, of order $\log\|x\|$ in dimension $d=4$, and of order 1 in dimensions $d\geq 5$. The corresponding weak convergences are also established. These results answer a question raised by Le Gall and Merle (Elect. Comm. in Probab. 11 (2006), 252-265).

math.PR↗
arXiv2025

hdbayes: An R Package for Bayesian Analysis of Generalized Linear Models Using Historical Data

There has been increased interest in the use of historical data to formulate informative priors in regression models. While many such priors for incorporating historical data have been proposed, adoption is limited due to access to software. Where software does exist, the implementations between different methods could be vastly different, making comparisons between methods difficult. In this paper, we introduce the R package hdbayes, an implementation of the power prior, normalized power prior, Bayesian hierarchical model, robust meta-analytic prior, commensurate prior, and latent exchangeability prior for generalized linear models. The bulk of the package is written in the Stan programming language, with user-friendly R wrapper functions to call samplers.

stat.ME↗
arXiv2025

Microcanonical cascades and random homeomorphisms

We give a complete solution to the Mandelbrot-Kahane problem for the microcanonical cascade measures by determing their exact Fourier dimensions. We also discuss the Frostman regularity as well as the bi-H\"older continuity of the Dubins-Freedman random homeomorphisms.

math.PR↗
arXiv2024

Minkowski sum of fractal percolation and random sets

In this paper, we prove that hitting probability of Minkowski sum of fractal percolations can be characterized by capacity. Then we extend this result to Minkowski sum of general random sets in $\mathbb Z^d$, including ranges of random walks and critical branching random walks, whose hitting probabilities are described by Newtonian capacity individually.

math.PR↗
arXiv2024

DriveGPT: Scaling Autoregressive Behavior Models for Driving

We present DriveGPT, a scalable behavior model for autonomous driving. We model driving as a sequential decision-making task, and learn a transformer model to predict future agent states as tokens in an autoregressive fashion. We scale up our model parameters and training data by multiple orders of magnitude, enabling us to explore the scaling properties in terms of dataset size, model parameters, and compute. We evaluate DriveGPT across different scales in a planning task, through both quantitative metrics and qualitative examples, including closed-loop driving in complex real-world scenarios. In a separate prediction task, DriveGPT outperforms state-of-the-art baselines and exhibits improved performance by pretraining on a large-scale dataset, further validating the benefits of data scaling.

cs.LG↗
arXiv2024

Branching brownian motion conditioned on large level sets

We study the precise large deviation probabilities for the sizes of intermediate level sets in branching Brownian motion (BBM). Our conclusions improve a result of A\"{i}dekon, Hu and Shi in [J. Math. Sci. \textbf{238}(2019)]. Additionally, we analyze the typical behaviors of BBM conditioned on large level sets. Our approach relies on the connections between intermediate level sets, additive martingale limits of BBM, and the global minimum of linearly transformed BBMs.

math.PR↗
arXiv2024

Harmonic analysis of Mandelbrot cascades -- in the context of vector-valued martingales

We solve a long-standing open problem of determining the Fourier dimension of the Mandelbrot canonical cascade measure (MCCM). This problem of significant interest was raised by Mandelbrot in 1976 and reiterated by Kahane in 1993. Specifically, we derive the exact formula for the Fourier dimension of the MCCM for random weights $W$ satisfying the condition $\mathbb{E}[W^t]<\infty$ for all $t>0$. As a corollary, we prove that the MCCM is Salem if and only if the random weight has a specific two-point distribution. In addition, we show that the MCCM is Rajchman with polynomial Fourier decay whenever the random weight satisfies $\mathbb{E}[W^{1+\delta}]<\infty$ for some $\delta>0$. As a consequence, we discover that, in the Biggins-Kyprianou's boundary case, the Fourier dimension of the MCCM exhibits a second order phase transition at the inverse temperature $\beta = 1/2$; we establish the upper Frostman regularity for MCCM; and we obtain a Fourier restriction estimate for MCCM. The major novelty of this paper is the discovery of putting the fine analysis of Fourier decay for multiplicative chaos measures into the theory of vector-valued martingales. This new viewpoint is of fundamental importance in the study of Fourier decay of multiplicative chaos measures. Indeed, in the sequel to this paper, combining the vector-valued martingale methods and ideas from Littlewood-Paley theory, the precise Fourier dimensions will be established for various classical models of multiplicative chaos measures including GMC of all dimensions, microcanonical Mandelbrot cascades, Mandelbrot random coverings, as well as Fourier-Walsh analysis of these models.

math.PR↗
arXiv2024

Branching random walk conditioned on large martingale limit

We consider a branching random walk in the non-boundary case where the additive martingale $W_n$ converges a.s. and in mean to some non-degenerate limit $W_\infty$. We first establish the joint tail distribution of $W_\infty$ and the global minimum of this branching random walk. Next, conditioned on the event that the minimum is atypically small or conditioned on very large $W_\infty$, we study the branching random walk viewed from the minimum and obtain the convergence in law in the vague sense. As a byproduct, we also get the right tail of the limit of derivative martingale.

math.PR↗
arXiv2023

Domain of attraction of the fixed points of Branching Brownian motion

We give a complete characterisation of the domain of attraction of fixed points of branching Brownian motion (BBM) with critical drift. Prior to this classification, we introduce a suitable metric space of locally finite point measures on which we prove 1) that the BBM with critical drift is a well-defined Markov process and 2) that it satisfies the Feller property. Several applications of this characterisation are given.

math.PR↗
arXiv2023

Nanoparticles Passive Targeting Allows Optical Imaging of Bone Diseases

Bone health related skeletal disorders are commonly diagnosed by X-ray imaging, but the radiation limits its use. Light excitation and optical imaging through the near-infrared-II window (NIR-II, 1000-1700 nm) can penetrate deep tissues without radiation risk, but the targeting of contrast agent is non-specific. Here, we report that lanthanide-doped nanocrystals can be passively transported by endothelial cells and macrophages from the blood vessels into bone marrow microenvironment. We found that this passive targeting scheme can be effective for longer than two months. We therefore developed an intravital 3D and high-resolution planar imaging instrumentation for bone disease diagnosis. We demonstrated the regular monitoring of 1 mm bone defects for over 10 days, with resolution similar to X-ray imaging result, but more flexible use in prognosis. Moreover, the passive targeting can be used to reveal the early onset inflammation at the joints as the synovitis in the early stage of rheumatoid arthritis. Furthermore, the proposed method is comparable to {\mu}CT in recognizing symptoms of osteoarthritis, including the mild hyperostosis in femur which is ~100 {\mu}m thicker than normal, and the growth of millimeter-scale osteophyte in the knee joint, which further proves the power and universality of our approach in diagnosis of bone diseases

physics.bio-ph↗