随机反转图的演化
The evolution of random reversal graph
摘要：
随机反转图提供了新的视角，允许研究基因组的连通性以及它们最可能的距离作为反转率的函数。我们的主要结果表明，在$λ_n=1/\binom{n+1}{2}$的随机反转图的结构发生了显着的变化。对于$λ_n=(1-ε)/\binom{n+1}{2}$，随机图由大小至多为$O(n\ln(n))$ a.s.的分量组成。对于$(1+ε)/\binom{n+1}{2}$，出现了唯一的最大组件，大小为$\sim \wp(ε) \cdot 2^n\cdot n$！$ a. s.这个“巨”分量在反转图中更密集。
英文摘要：
The random reversal graph offers new perspectives, allowing to study the connectivity of genomes as well as their most likely distance as a function of the reversal rate. Our main result shows that the structure of the random reversal graph changes dramatically at $λ_n=1/\binom{n+1}{2}$. For $λ_n=(1-ε)/\binom{n+1}{2}$, the random graph consists of components of size at most $O(n\ln(n))$ a.s. and for $(1+ε)/\binom{n+1}{2}$, there emerges a unique largest component of size $\sim \wp(ε) \cdot 2^n\cdot n$!$ a.s.. This "giant" component is furthermore dense in the reversal graph.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
