# Difference between revisions of "Probability Seminar"

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:Abstract: Finite (or fixed) rank perturbations of large random matrices arise in a number of applications. The main phenomenon is a phase transition in the largest eigenvalues as a function of the strength of the perturbation. I will describe joint work with Bálint Virág in which we introduce a new way to study these models. The starting point is a reduction to a natural band form; under the soft edge scaling, it converges to a souped-up version of the known continuum random Schrödinger operator on the half-line. We describe the near-critical fluctuations in several ways, solving a known open problem in the real case. One characterization also yields a new route to the Painlevé structure in the celebrated Tracy-Widom laws. | :Abstract: Finite (or fixed) rank perturbations of large random matrices arise in a number of applications. The main phenomenon is a phase transition in the largest eigenvalues as a function of the strength of the perturbation. I will describe joint work with Bálint Virág in which we introduce a new way to study these models. The starting point is a reduction to a natural band form; under the soft edge scaling, it converges to a souped-up version of the known continuum random Schrödinger operator on the half-line. We describe the near-critical fluctuations in several ways, solving a known open problem in the real case. One characterization also yields a new route to the Painlevé structure in the celebrated Tracy-Widom laws. | ||

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− | + | UW Math Probability Seminar Fall 2011 | |

− | : | + | Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. |

− | + | Organized by Benedek Valkó | |

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− | + | Past Seminars | |

− | + | Schedule and Abstracts | |

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− | == | + | == Thursday, September 15, Jun Yin, University of Wisconsin - Madison == |

− | + | '''Some recent results on random matrices with almost independent entries.''' | |

− | |||

− | + | In this talk, we are going to introduce some recent work on a large class of random matrices, whose entries are (almost) independent. For example, the Wigner matrix, generalized Wigner matrix, Band random matrix, Covariance matrix and Sparse random matrix. We mainly focus on the local statistics of the eigenvalues and eigenvectors of these random matrix ensembles. We will also introduce some applications of these results and some long-standing open questions. | |

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− | + | == Thursday, September 22, Philip Matchett Wood, University of Wisconsin - Madison == | |

− | + | TBA | |

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− | + | TBA | |

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− | + | == Thursday, September 29, Antonio Auffinger, University of Chicago == | |

− | + | TBA | |

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− | + | TBA | |

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− | : | + | |

+ | == Tuesday, October 4, 2:30 PM, Gregorio Moreno Flores, University of Wisconsin - Madison == | ||

+ | <span style="color:#FF0000">'''UNUSUAL TIME'''<span style="color:#009000"> | ||

+ | |||

+ | TBA | ||

+ | |||

+ | TBA | ||

+ | |||

+ | |||

+ | |||

+ | == Thursday, October 13, No seminar because of the MIDWEST PROBABILITY COLLOQUIUM == | ||

+ | |||

+ | |||

+ | |||

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+ | == Thursday, October 20, Kay Kirkpatrick, University of Illinois at Urbana-Champaign == | ||

+ | |||

+ | TBA | ||

+ | |||

+ | TBA | ||

+ | |||

+ | |||

+ | |||

+ | == Thursday, October 27, No seminar this week == | ||

+ | |||

+ | |||

+ | |||

+ | |||

+ | == Monday, October 31, 2:30pm, Ankit Gupta, Ecole Polytechnique, Centre de Mathematiques Appliqees == | ||

+ | <span style="color:#FF0000">'''UNUSUAL TIME'''<span style="color:#009000"> | ||

+ | |||

+ | TBA | ||

+ | |||

+ | TBA | ||

+ | |||

+ | |||

+ | |||

+ | == Friday, November 4, 2:30pm, Michael Cranston, University of California, Irvine == | ||

+ | <span style="color:#FF0000">'''UNUSUAL TIME'''<span style="color:#009000"> | ||

+ | |||

+ | TBA | ||

+ | |||

+ | TBA | ||

+ | |||

+ | |||

+ | |||

+ | == Thursday, November 24, No seminar because of THANKSGIVING == |

## Revision as of 11:28, 9 September 2011

## Spring 2011

Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. If you would like to receive announcements about upcoming seminars, please visit this page to sign up for the email list.

## Monday, January 24, 2:25PM, B129 Sunil Chhita (Brown University)

**UNUSUAL TIME AND PLACE**

- Title:
**Particle Systems arising from an Anti-ferromagnetic Ising Model**

- Abstract: We present a low temperature anisotropic anti-ferromagnetic 2D Ising model through the guise of a certain dimer model. This model also has a bijection with a one-dimensional particle system equipped with creation and annihilation. We can find the exact phase diagram, which determines two significant values (the independent and critical value). We also highlight some of the behavior of the model in the scaling window at criticality and at independence.

## Thursday, February 10, Alex Bloemendal (Toronto)

- Title:
**Finite rank perturbations of large random matrices**

- Abstract: Finite (or fixed) rank perturbations of large random matrices arise in a number of applications. The main phenomenon is a phase transition in the largest eigenvalues as a function of the strength of the perturbation. I will describe joint work with Bálint Virág in which we introduce a new way to study these models. The starting point is a reduction to a natural band form; under the soft edge scaling, it converges to a souped-up version of the known continuum random Schrödinger operator on the half-line. We describe the near-critical fluctuations in several ways, solving a known open problem in the real case. One characterization also yields a new route to the Painlevé structure in the celebrated Tracy-Widom laws.

UW Math Probability Seminar Fall 2011

Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted.

Organized by Benedek Valkó

Past Seminars

Schedule and Abstracts

## Thursday, September 15, Jun Yin, University of Wisconsin - Madison

**Some recent results on random matrices with almost independent entries.**

In this talk, we are going to introduce some recent work on a large class of random matrices, whose entries are (almost) independent. For example, the Wigner matrix, generalized Wigner matrix, Band random matrix, Covariance matrix and Sparse random matrix. We mainly focus on the local statistics of the eigenvalues and eigenvectors of these random matrix ensembles. We will also introduce some applications of these results and some long-standing open questions.

## Thursday, September 22, Philip Matchett Wood, University of Wisconsin - Madison

TBA

TBA

## Thursday, September 29, Antonio Auffinger, University of Chicago

TBA

TBA

## Tuesday, October 4, 2:30 PM, Gregorio Moreno Flores, University of Wisconsin - Madison

**UNUSUAL TIME**

TBA

TBA

## Thursday, October 13, No seminar because of the MIDWEST PROBABILITY COLLOQUIUM

## Thursday, October 20, Kay Kirkpatrick, University of Illinois at Urbana-Champaign

TBA

TBA

## Thursday, October 27, No seminar this week

## Monday, October 31, 2:30pm, Ankit Gupta, Ecole Polytechnique, Centre de Mathematiques Appliqees

**UNUSUAL TIME**

TBA

TBA

## Friday, November 4, 2:30pm, Michael Cranston, University of California, Irvine

**UNUSUAL TIME**

TBA

TBA

== Thursday, November 24, No seminar because of THANKSGIVING ==