Strong limit theorems in the multi-color generalized allocation scheme
Alexey Chuprunov, Istv\'an Fazekas
TL;DR
This paper extends the generalized allocation scheme to include colored balls and establishes analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers for the count of boxes with a fixed number of balls.
Contribution
It introduces a colored extension of the allocation scheme and proves new strong limit theorems for the distribution of balls in boxes.
Findings
Analogues of the Law of the Iterated Logarithm established
Strong Law of Large Numbers proved for colored schemes
Results applicable to fixed numbers of balls in boxes
Abstract
The generalized allocation scheme is studied. Its extension for coloured balls is defined. Some analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers are obtained for the number of boxes containing fixed numbers of balls.
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
TopicsLimits and Structures in Graph Theory · Mathematical Dynamics and Fractals · Markov Chains and Monte Carlo Methods