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Random hypergraph is a broad concept used to describe probabilitydistributions over hypergraphs, which are mathematical structures withapplications in various fields, e.g., complex systems in physics, computerscience, social sciences, and network science. Ensemble methods, on the otherhand, are crucial both in physics and machine learning. In physics, ensembletheory helps bridge the gap between the microscopic and macroscopic worlds,providing a statistical framework for understanding systems with a vast numberof particles. In machine learning, ensemble methods are valuable because theyimprove predictive accuracy, reduce overfitting, lower prediction variance,mitigate bias, and capture complex relationships in data. However, there islimited research on applying ensemble methods to a set of random hypergraphs.This work aims to study the connectivity behavior of an ensemble of randomhypergraphs. Specifically, it focuses on quantifying the random behavior of thealgebraic connectivity of these ensembles through tail bounds. We utilizeLaplacian tensors to represent these ensemble random hypergraphs and establishmathematical theorems, such as Courant-Fischer and Lieb-Seiringer theorems fortensors, to derive tail bounds for the algebraic connectivity. We derive threedifferent tail bounds, i.e., Chernoff, Bennett, and Bernstein bounds, for thealgebraic connectivity of ensemble hypergraphs with respect to different randomhypergraphs assumptions.

Algebraic Connectivity Characterization of Ensemble Random Hypergraphs