11 problems

Let leaf-$\mathrm{PA}(a)$ be the growing random-tree model in which new vertices attach to existing vertices at rate $\ell+a$, where $\ell$ is the leaf degree and $a>0$. Let…

The observed event-size distributions of human conflict are approximately power-law across much of their range. Self-organization conjecture. The common structure of these observed…

Let $d=4$, let $m(\ell)\asymp\ell^{-\beta}$ be the worm-length mass function, and let $v_c$ denote the critical intensity. Four-dimensional worm-percolation conjecture. One has … T…

Let $d=3$, let $m(\ell)\asymp\ell^{-\beta}$ be the worm-length mass function, and let $v_c$ denote the critical intensity. Three-dimensional worm-percolation conjecture. One has ……

Consider the discrete-space process on $\mathbb{Z}^{\mathbb{Z}_+}$ with birth rate … where $a_{\mathrm{pow}}(x)=c_{\mathrm{pow}}/(|x|+1)^\alpha$ for $x\ne0$,…

Expected second-degree distribution conjecture. For

In a text, rank word types from most to least frequent and let $q(s_m)$ denote the probability of observing the $m$-th most common word. Zipf's law is the power-law distribution ……

The paper studies power-law random graphs in the finite-mean, infinite-variance regime, including a conditionally Poissonian random graph with i.i.d. Pareto-distributed capacities.…

Modulated branching processes and related randomly evolving population models produce power-law distributions, and can therefore be used to model bursts of requests at popular Inte…

Let r_k_{k\geq 1} be the distribution of the initial degrees in the PARID model, and suppose that it is a power-law distribution with exponent…

Let the initial degrees have a power-law distribution with infinite mean, and let the resulting graph be generated by the preferential attachment model described in the paper. Infi…