##### Department of Mathematics,

University of California San Diego

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### Graduate Students in Probability Seminar

## Yizhe Zhu

#### UCSD

## Community detection in sparse random hypergraphs

##### Abstract:

The stochastic block model (SBM) is a generative model for random graphs with a community structure, which has been one of the most fruitful research topics in community detection and clustering. A phase transition behavior for detection was conjecured by Decelle el al. (2011), and was confirmed by Mossel et al. (2012,2013) and Massouli\'e (2013). We consider the community detection problem in random hypergraphs. Angelini et al. (2015) conjectured a phase transition for community detection in sparse hypergraphs generated by a hypergraph stochastic block model (HSBM). We confirmed the positive part of the phase transition for the 2-block case by a generalization of the method developed in Massouli\'e (2013). We introduced a matrix which counts self-avoiding walks on hypergraphs, whose leading eigenvectors give us a correlated reconstruction. This is joint work with Soumik Pal.

### October 21, 2019

### 10:00 AM

### AP&M 5829

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