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Abstract. This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. The limit theorems are universal depending solely on the limiting behavior of the ratio of the number of edges in the graph and the number of colors, and works for any graph sequence deterministic or random. The proofs are based on moment calculations which relates to results of Erdős and Alon on extremal subgraph counts. As a byproduct of our calculations a simple new proof of a result of Alon, estimating the number of isomorphic copies of a cycle of given length in graphs with fixed number of edges, is presented. 1.

In the current paper, we propose a modeling framework to explicitly link a count data model with an event type multinomial choice model. The proposed framework uses a multinomial probit kernel for the event type choice model and introduces unobserved heterogeneity in both the count and discrete choice components. Additionally, this paper establishes several new results regarding the distribution of the maximum of multivariate normally distributed variables, which form the basis to embed the multinomial probit model within a joint modeling system for multivariate count data. The model is applied for analyzing out-of-home non-work episodes pursued by workers, using data from the National Household Travel Survey.

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