Purpose: This paper aims to formalize long-term trajectories of human civilization as a scientific and ethical field of study. The long-term trajectory of human civilization can be defined as the path that human civilization takes during the entire future time period in which human civilization...

Purpose: This paper aims to contribute to the futurology of a possible artificial intelligence (AI) breakthrough, by reexamining the Omohundro–Bostrom theory for instrumental vs final AI goals. Does that theory, along with its predictions for what a superintelligent AI would be motivated to...

We consider Glauber dynamics at zero temperature for the ferromagnetic Ising model on the usual random graph model on N vertices, with on average γ edges incident to each vertex, in the limit as N→∞. Based on numerical simulations, Svenson (Phys. Rev. E 64 (2001) 036122) reported that the...

Consider the random-cluster model on the integer lattice with parameters p and q. As p, q --> 0 in such a way that q/p --> 0, the random-cluster measures converge weakly to the uniform spanning tree measure of Pemantle (1991).

We consider the random coloring of the vertices of a graph G, that arises by first performing i.i.d. bond percolation with parameter p on G, and then assigning a random color, chosen according to some prescribed probability distribution on the finite set {0,...,r-1}, to each of the connected...

We study the two-type Richardson model on , d[greater-or-equal, slanted]2, in the asymmetric case where the two particle types have different infection rates. Starting with a single particle of each type, and fixing the infection rate for one of the types, we show that mutual unbounded growth...