论文标题
具有添加剂适应性的优先附着模型的相变
A phase transition for preferential attachment models with additive fitness
论文作者
论文摘要
优先依恋模型构成了流行的成长网络类别，其中传入的顶点优选地连接到高度的顶点。我们考虑了此过程的一种变体，其中顶点配备了随机的初始适应性，代表顶点之间的初始不均匀性，并且健身性以添加剂方式影响顶点的吸引力。我们考虑了重尾适应性分布，并表明该模型取决于健身分布的尾部指数。在弱混乱状态下，旧顶点之一具有最大程度的程度，而对于强大的疾病，具有最大程度的顶点必须满足健身和年龄之间的适当平衡。我们的方法使用Martingale方法来显示学位的集中度以及极值理论以控制健身景观。
Preferential attachment models form a popular class of growing networks, where incoming vertices are preferably connected to vertices with high degree. We consider a variant of this process, where vertices are equipped with a random initial fitness representing initial inhomogeneities among vertices and the fitness influences the attractiveness of a vertex in an additive way. We consider a heavy-tailed fitness distribution and show that the model exhibits a phase transition depending on the tail exponent of the fitness distribution. In the weak disorder regime, one of the old vertices has maximal degree irrespective of fitness, while for strong disorder the vertex with maximal degree has to satisfy the right balance between fitness and age. Our methods use martingale methods to show concentration of degree evolutions as well as extreme value theory to control the fitness landscape.
