## Abstract

In this work we examine the behavior of the minimum singular value of random Vandermonde matrices. In particular, we prove that the minimum singular value s _{1}(N) is at most N exp(-C√N) where N is the dimension of the matrix and C is a constant. Furthermore, the value of the constant C is determined explicitly. The main result is obtained in two different ways. One approach uses techniques from stochastic processes and in particular, a construction related to the Brownian bridge. The other one is a more direct analytical approach involving combinatorics and complex analysis. As a consequence, we obtain a lower bound on the maximum absolute value of a random polynomial on the unit circle, which may be of independent mathematical interest.

Original language | English |
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Title of host publication | 2012 IEEE international symposium on information theory proceedings, ISIT 2012 |

Place of Publication | Piscataway, NJ |

Publisher | Institute of Electrical and Electronics Engineers (IEEE) |

Pages | 2441-2445 |

Number of pages | 5 |

ISBN (Electronic) | 9781467325790 |

ISBN (Print) | 9781467325806 |

DOIs | |

Publication status | Published - 2012 |

Externally published | Yes |

Event | 2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States Duration: 1 Jul 2012 → 6 Jul 2012 |

### Other

Other | 2012 IEEE International Symposium on Information Theory, ISIT 2012 |
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Country/Territory | United States |

City | Cambridge, MA |

Period | 1/07/12 → 6/07/12 |