On a memory game and preferential attachment graphs
Huseyin Acan, Pawel Hitczenko

TL;DR
This paper analyzes the asymptotic distributions of parameters in a memory game, linking it to preferential attachment graphs and providing new proofs for known results in graph degree distributions.
Contribution
It extends previous work by deriving limiting distributions for memory game parameters and connecting these to preferential attachment graph models with simplified proofs.
Findings
Game length converges to a normal distribution.
Waiting time for first match converges to a Rayleigh distribution.
Number of lucky moves converges to a Poisson distribution.
Abstract
In a recent paper Velleman and Warrington analyzed the expected values of some of the parameters in a memory game, namely, the length of the game, the waiting time for the first match, and the number of lucky moves. In this paper we continue this direction of investigation and obtain the limiting distributions of those parameters. More specifically, we prove that when suitably normalized, these quantities converge in distribution to a normal, Rayleigh, and Poisson random variable, respectively. We also make a connection between the memory game and one of the models of preferential attachment graphs. In particular, as a by--product of our methods we obtain simpler proofs (although without rate of convergence) of some of the results of Pek\"oz, R\"ollin, and Ross on the joint limiting distributions of the degrees of the first few vertices in preferential attachment graphs. For proving…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStochastic processes and statistical mechanics · Complex Network Analysis Techniques · Game Theory and Applications
