发表机构
Johannes Gutenberg-Universität Mainz（约翰内斯·古腾堡美因茨大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过局部到全局比较原理，证明了有限寿命青蛙模型在超线性增长图上的临界密度曲线连续且严格递减，并具有局部双Lipschitz正则性，解决了相关猜想并扩展到长程模型。
AI 中文摘要
我们研究有限寿命青蛙模型的相边界。对于无限、连通、局部有限的传递图上的速率为一的连续时间简单随机游走，且图具有超线性增长，我们证明了临界密度曲线是连续且严格递减的，并且$ -\log\lambda_c$是局部双Lipschitz的。逆临界寿命曲线在其有限的任何地方具有相应的正则性。每当每个正密度具有有限的临界寿命时，这解决了Angel、de la Riva、Hermon和Shi关于临界参数曲线正则性的猜想；特别是，在非可安培和超线性多项式增长的图上，这一结论成立。我们还建立了小寿命缩放极限，并将临界曲线正则性和尖锐性扩展到一类长程青蛙模型。主要工具是对于由独立有限根范围生成的激活过程的局部到全局原理：局部一击比较意味着全局可达性和存活性的比较。
英文摘要
We study the phase boundary of the finite-lifespan frog model. For rate-one continuous-time simple random walk on an infinite, connected, locally finite transitive graph of superlinear growth, we prove that the critical-density curve is continuous and strictly decreasing, with $-\logλ_c$ locally bi-Lipschitz. The inverse critical-lifespan curve has the corresponding regularity wherever it is finite. Thus the critical-curve conjecture of Angel, de la Riva, Hermon, and Shi reduces to finiteness of the critical lifespan at every positive density. We identify the exact short-lifespan limit $tλ_c(t)\toΔ\log(1/(1-p_c(G)))$, where $Δ$ is the degree and $p_c(G)$ is the bond-percolation threshold, and extend critical-curve regularity and sharpness to a class of long-range frog models. The main tool is a local-to-global principle for activation processes generated by independent finite rooted ranges: local one-hit comparison implies comparison of global reachability and survival. The comparison allows disconnected ranges and source-dependent laws, and therefore also applies to activation models beyond random walks on a fixed graph.
Comments39 pages, no figures. v2: identifies the exact short-lifespan constant in Theorem A and Proposition 5.3; clarifies several proofs, including the long-range sharpness exploration; updates references and exposition
