Randomized rumor spreading processes diffuse information on an undirected graph and have been widely studied. In this work, we present a generic framework for analyzing a broad class of such processes on regular graphs. Our analysis is protocol-agnostic, as it only requires the expected proportion of newly informed vertices in each round to be bounded, and a natural negative correlation property. This framework allows us to analyze various protocols, including PUSH, PULL, and PUSH-PULL, thereby extending prior research. Unlike previous work, our framework accommodates message failures at any time $t\geq 0$ with a probability of $1-q(t)$, where the credibility $q(t)$ is any function of time. This enables us to model real-world scenarios in which the transmissibility of rumors may fluctuate, as seen in the spread of ``fake news'' and viruses. Additionally, our framework is sufficiently broad to cover dynamic graphs.

翻译：随机谣言传播过程在无向图上扩散信息，已被广泛研究。本文针对正则图上一大类此类过程提出通用分析框架。该分析具有协议无关性，仅需保证每轮新知情顶点期望比例有界，且满足自然负相关性质。该框架可分析包括PUSH、PULL和PUSH-PULL在内的多种协议，拓展了既有研究。与前期工作不同，本文框架允许消息在任意时间$t\geq 0$以概率$1-q(t)$失效，其中可信度$q(t)$为时间的任意函数。这使我们能模拟谣言传播能力可能波动的现实场景，如"假新闻"与病毒的传播。此外，本框架还可覆盖动态图情形。