Emmanuel Akame Mfoumou

arXiv2026

Accelerated Simulation Algorithms for Extreme First-Passage Problems with General Emission Profiles

Fastest arrival events, where the first among many diffusing particles reaches a target, are central in triggering signal initiation in molecular stochastic systems. Classical approaches to simulate such events rely on full trajectory generation of all particles, leading to prohibitive computational costs in the large particle number regime. In this work, we present a general simulation framework for efficiently generating order statistics of arrival times by exploiting asymptotic first-passage distributions. This framework applies to diffusion processes in bounded domains with localized absorbing targets, for which short-time first-passage asymptotics are available, such as Brownian motion in dimensions one, two, and three. Starting with the case of instantaneous emission, we derive and implement a recursive inverse transform algorithm to simulate the first $k$ arrivals without tracking particle trajectories. We extend this algorithm to time-dependent emission profiles via an iterative approach, enabling the simulation of extreme statistics in systems with temporal injection, ranging from rapid to prolonged emission. Additionally, we provide asymptotic estimates of the mean fastest arrival time. To conclude, the present acceleration algorithm which bypasses Brownian simulations of trajectories can be used for spatial reaction networks, rare event detection, or diffusion-controlled activation.

math.PR↗

arXiv2025

Assessing One-Dimensional Cluster Stability by Extreme-Point Trimming

We develop a probabilistic method for assessing the tail behavior and geometric stability of one-dimensional n i.i.d. samples by tracking how their span contracts when the most extreme points are trimmed. Central to our approach is the diameter-shrinkage ratio, that quantifies the relative reduction in data range as extreme points are successively removed. We derive analytical expressions, including finite-sample corrections, for the expected shrinkage under both the uniform and Gaussian hypotheses, and establish that these curves remain distinct even for moderate number of removal. We construct an elementary decision rule that assigns a sample to whichever theoretical shrinkage profile it most closely follows. This test achieves higher classification accuracy than the classical likelihood-ratio test in small-sample or noisy regimes, while preserving asymptotic consistency for large n. We further integrate our criterion into a clustering pipeline (e.g. DBSCAN), demonstrating its ability to validate one-dimensional clusters without any density estimation or parameter tuning. This work thus provides both theoretical insight and practical tools for robust distributional inference and cluster stability analysis.

stat.ML↗