Related papers: On a memory game and preferential attachment graph…
We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree…
For a sequence of random graphs, the limit law we refer to is the existence of a limiting probability of any graph property that can be expressed in terms of predicate logic. A zero-one limit law is shown by Shelah and Spencer for…
We consider the preferential attachment model. This is a growing random graph such that at each step a new vertex is added and forms $m$ connections. The neighbors of the new vertex are chosen at random with probability proportional to…
We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment…
We study preferential attachment models where vertices enter the network with i.i.d. random numbers of edges that we call the out-degree. We identify the local limit of such models, substantially extending the work of Berger et al.(2014).…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
We study a random game in which two players in turn play a fixed number of moves. For each move, there are two possible choices. To each possible outcome of the game we assign a winner in an i.i.d. fashion with a fixed parameter p. In the…
We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…
This paper reframes approachability theory within the context of population games. Thus, whilst one player aims at driving her average payoff to a predefined set, her opponent is not malevolent but rather extracted randomly from a…
The preference graph is a combinatorial representation of the structure of a normal-form game. Its nodes are the strategy profiles, with an arc between profiles if they differ in the strategy of a single player, where the orientation…
Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…
We introduce a novel preferential attachment model using the draw variables of a modified P\'olya urn with an expanding number of colors, notably capable of modeling influential opinions (in terms of vertices of high degree) as the graph…
We study the joint degree counts in proportional attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak convergence with respect to the p-norm topology for appropriate p…
Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference,for instance GLM techniques, and model verification methods will require knowing test statistics are…
We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…
Preferential attachment is a popular generative mechanism to explain the widespread observation of power law distributed networks. We introduce an alternative explanation for the phenomenon by allowing the link growth rates to vary across…
We continue our studies of burn-off chip-firing games from [Discrete Math. Theor. Comput. Sci. 15 (2013), no. 1, 121-132; MR3040546] and [Australas. J. Combin. 68 (2017), no. 3, 330-345; MR3656659]. The latter article introduced randomness…
Merging asymptotic expansions of arbitrary length are established for the distribution functions and for the probabilities of suitably centered and normalized cumulative winnings in a full sequence of generalized St. Petersburg games,…
We study logical limit laws for preferential attachment random graphs. In this random graph model, vertices and edges are introduced recursively: at time $1$, we start with vertices $0,1$ and $m$ edges between them. At step $n+1$ the vertex…