# Difference between revisions of "Past Probability Seminars Spring 2020"

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'''A simplified proof of the relation between scaling exponents in first passage percolation''' | '''A simplified proof of the relation between scaling exponents in first passage percolation''' | ||

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In first passage percolation, we place i.i.d. non-negative weights on the nearest-neighbor edges of Z^d and study the induced random metric. A long-standing conjecture gives a relation between two "scaling exponents": one describes the variance of the distance between two points and the other describes the transversal fluctuations of optimizing paths between the same points. In a recent breakthrough work, Sourav Chatterjee proved a version of this conjecture using a strong definition of the exponents. I will discuss work I just completed with Michael Damron, in which we introduce a new and intuitive idea that replaces Chatterjee's main argument and gives an alternative proof of the scaling relation. One advantage of our argument is that it does not require a non-trivial technical assumption of Chatterjee on the weight distribution. | In first passage percolation, we place i.i.d. non-negative weights on the nearest-neighbor edges of Z^d and study the induced random metric. A long-standing conjecture gives a relation between two "scaling exponents": one describes the variance of the distance between two points and the other describes the transversal fluctuations of optimizing paths between the same points. In a recent breakthrough work, Sourav Chatterjee proved a version of this conjecture using a strong definition of the exponents. I will discuss work I just completed with Michael Damron, in which we introduce a new and intuitive idea that replaces Chatterjee's main argument and gives an alternative proof of the scaling relation. One advantage of our argument is that it does not require a non-trivial technical assumption of Chatterjee on the weight distribution. |

## Revision as of 14:04, 16 September 2011

## Fall 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.

## 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

**Survey of the Circular Law**

What do the eigenvalues of a random matrix look like? This talk will focus on large square matrices where the entries are independent, identically distributed random variables. In the most basic case, the distribution of the eigenvalues in the complex plane (suitably scaled) approaches the uniform distribution on the unit disk, which is called the circular law. We will discuss some of the methods that have been used to prove the circular law, including recent work that has extended the circular law to the most general situation, and we will also discuss generalizations to situations where the eigenvalue distributions are stable, but non-circular.

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

**A simplified proof of the relation between scaling exponents in first passage percolation**

In first passage percolation, we place i.i.d. non-negative weights on the nearest-neighbor edges of Z^d and study the induced random metric. A long-standing conjecture gives a relation between two "scaling exponents": one describes the variance of the distance between two points and the other describes the transversal fluctuations of optimizing paths between the same points. In a recent breakthrough work, Sourav Chatterjee proved a version of this conjecture using a strong definition of the exponents. I will discuss work I just completed with Michael Damron, in which we introduce a new and intuitive idea that replaces Chatterjee's main argument and gives an alternative proof of the scaling relation. One advantage of our argument is that it does not require a non-trivial technical assumption of Chatterjee on the weight distribution.

## 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 ==