The Poset of Hypergraph Quasirandomness

Chung and Graham began the systematic study of k-uniform hypergraph quasirandom properties soon after the foundational results of Thomason and Chung-Graham-Wilson on quasirandom graphs. One feature that became apparent in the early work on k-uniform hypergraph quasirandomness is that properties that are equivalent for graphs are not equivalent for hypergraphs, and thus hypergraphs enjoy a variety of inequivalent quasirandom properties. In the past two decades, there has been an intensive study of these disparate notions of quasirandomness for hypergraphs, and an open problem that has emerged is to determine the relationship between them. Our main result is to determine the poset of implications between these quasirandom properties. This answers a recent question of Chung and continues a project begun by Chung and Graham in their first paper on hypergraph quasirandomness in the early 1990's.Comment: 43 pages, 1 figur

Some singular sample path properties of a multiparameter fractional Brownian motion

We prove a Chung-type law of the iterated logarithm for a multiparameter extension of the fractional Brownian motion which is not increment stationary. This multiparameter fractional Brownian motion behaves very differently at the origin and away from the axes, which also appears in the Hausdorff dimension of its range and in the measure of its pointwise H\"older exponents. A functional version of this Chung-type law is also provided.Comment: 21 pages. To appear in J. Theoret. Proba

The Fundamental Interests of Citizens: A Response to Chung

Hun Chung’s recent article “Rawls’s Self-Defeat: A Formal Analysis” argues that the selection of results equivalent to justice as fairness can be derived by utilitarianism. Chung argues that these results can be achieved through the use of Rawls’s constructed utility function from his work Justice as Fairness. Although Chung’s article is finely argued and presented in great detail, this paper will show that Chung made three mistakes in the fundamentals of his argument. First, Chung mistakes Rawls’s constructed utility function as actually utilitarian. Second, Chung confuses the motivations and the assumptions of those held by agents in the original position and those held by utilitarian agents. Last, Chung’s previous mistakes result in the incorrect conclusion that an equal distribution of resources will be selected by representative agents instead of the unequal distribution prescribed by the difference principle

On three-dimensional topological field theories constructed from Dω(G)D^\omega(G) for finite group

We investigate the 3d lattice topological field theories defined by Chung, Fukuma and Shapere. We concentrate on the model defined by taking a deformation \D{G} of the quantum double of a finite commutative group $G$ as the underlying Hopf algebra. It is suggested that Chung-Fukuma-Shapere partition function is related to that of Dijkgraaf-Witten by \zcfs = |\zdw|^2 when $G=\Z_{2N+1}$. For $G=\Z_{2N}$, such a relation does not hold.Comment: 13 pages, 3 PS figures include

Letter from Connie Chung to Geraldine Ferraro

Handwritten letter from Connie Chung, NBC News, to Geraldine Ferraro, thanking Ferraro for her interview.https://ir.lawnet.fordham.edu/vice_presidential_campaign_correspondence_1984_personal/1008/thumbnail.jp

New Lower Bounds for Some Multicolored Ramsey Numbers

We use finite fields and extend a result of Fan Chung to give eight new, nontrivial, lower bounds.Comment: 6 page