## Abstract

High dimensional expanders is a vibrant emerging field of study. Nevertheless, the only known construction of bounded degree high dimensional expanders is based on Ramanujan complexes, whereas one dimensional bounded degree expanders are abundant. In this work we construct new families of bounded degree high dimensional expanders obeying the local spectral expansion property. A property that implies, geometric overlapping, fast mixing of high dimensional random walks, agreement testing and agreement expansion. The construction also yields new families of expander graphs. The construction is quite elementary and it is presented in a self contained manner; This is in contrary to the highly involved construction of the Ramanujan complexes. The construction is also strongly symmetric; The symmetry of the construction could be used, for example, to obtain good symmetric LDPC codes that were previously based on Ramanujan graphs.

Original language | English |
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Title of host publication | STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing |

Editors | Monika Henzinger, David Kempe, Ilias Diakonikolas |

Publisher | Association for Computing Machinery |

Pages | 952-963 |

Number of pages | 12 |

ISBN (Electronic) | 9781450355599 |

DOIs | |

State | Published - 20 Jun 2018 |

Event | 50th Annual ACM Symposium on Theory of Computing, STOC 2018 - Los Angeles, United States Duration: 25 Jun 2018 → 29 Jun 2018 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0737-8017 |

### Conference

Conference | 50th Annual ACM Symposium on Theory of Computing, STOC 2018 |
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Country/Territory | United States |

City | Los Angeles |

Period | 25/06/18 → 29/06/18 |

### Bibliographical note

Publisher Copyright:© 2018 Association for Computing Machinery.

## Keywords

- High dimensional expanders
- Simplicial complexes
- Spectral gap