We give a simple rigourous treatment of the classical results of the abelian sandpile model. Although we treat results which are well-known in the physics literature, in many cases we did not findâ€¦ (More)

We study random graphs with an i.i.d. degree sequence of which the tail of the distribution function F is regularly varying with exponent Ï„ âˆˆ (1, 2). Thus, the degrees have infinite mean. Such randomâ€¦ (More)

In this paper we study random graphs with independent and identically distributed degrees of which the tail of the distribution function is regularly varying with exponent Ï„ âˆˆ (2, 3). The number ofâ€¦ (More)

In this paper we study distances and connectivity properties of random graphs with an arbitrary i.i.d. degree sequence. When the tail of the degree distribution is regularly varying with exponent 1 âˆ’â€¦ (More)

Consider the following evolution model, proposed in [3] by Bak and Sneppen. Put N vertices on a circle, spaced evenly. Each vertex represents a certain species. We associate with each vertex a randomâ€¦ (More)

In this paper, we study the configuration model (CM) with i.i.d. degrees. We establish a phase transition for the diameter when the power-law exponent Ï„ of the degrees satisfies Ï„ âˆˆ (2, 3). Indeed,â€¦ (More)

In this paper we derive results concerning the connected components and the diameter of random graphs with an arbitrary i.i.d. degree sequence. We study these properties primarily, but notâ€¦ (More)

In this paper we study distances and connectivity properties of random graphs with an arbitrary i.i.d. degree sequence. When the tail of the degree distribution is regularly varying with exponent 1 âˆ’â€¦ (More)