Department of

# Mathematics

Seminar Calendar
for Graduate Probability Seminar events the year of Monday, February 11, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2019          February 2019            March 2019
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5                   1  2                   1  2
6  7  8  9 10 11 12    3  4  5  6  7  8  9    3  4  5  6  7  8  9
13 14 15 16 17 18 19   10 11 12 13 14 15 16   10 11 12 13 14 15 16
20 21 22 23 24 25 26   17 18 19 20 21 22 23   17 18 19 20 21 22 23
27 28 29 30 31         24 25 26 27 28         24 25 26 27 28 29 30
31


Thursday, January 24, 2019

2:00 pm in 347 Altgeld Hall,Thursday, January 24, 2019

#### Introduction to Percolation Theory

###### Grigory Terlov (UIUC Math)

Abstract: This is the first part of two talks designed to introduce students to Percolation Theory. We will describe the model, talk about infinite clusters, prove the existence of the phase transition, introduce the universality principle and more.

Thursday, January 31, 2019

2:00 pm in 347 Altgeld Hall,Thursday, January 31, 2019

#### Introduction to Percolation Theory (Part 2)

###### Grigory Terlov (UIUC Math)

Abstract: This is the second part of two talks designed to introduce students to Percolation Theory. We will discuss an upper bound for critical probability for $\mathbb{Z}^d$ via cut-sets and duality. This talk should be accessible for people who missed the first part.

Thursday, February 7, 2019

2:00 pm in 347 Altgeld Hall,Thursday, February 7, 2019

#### An Introduction to Dyson Brownian Motion and Universality

###### Kesav Krishnan (UIUC Math)

Abstract: We define Brownian motion on the space of N×N Hermitian Matrices, and derive an SDE for the corresponding process of the eigenvalues. We then establish that the eigenvalue process is identical to Brownian motion in R^n confined to the Weyl Chamber.

Thursday, February 14, 2019

2:00 pm in 347 Altgeld Hall,Thursday, February 14, 2019

#### An Introduction to Dyson Brownian Motion and Universality (Part 2)

###### Kesav Krishnan (UIUC Math)

Abstract: We will discuss the connections of Dyson Brownian Motion and the Totally Asymmetric Simple Exclusion Process (TASEP). This will be the first glimpse of the Kardar Parisi Zhang Universality class.

Thursday, April 11, 2019

2:00 pm in 347 Altgeld Hall,Thursday, April 11, 2019

#### Local Limit Theorem

###### Qiang Wu (UIUC Math)

Abstract: This talk is an introduction to some classical CLT variants, specifically on local limit theorem (LLT). The proof of classical LLT for lattice and non-lattice distribution will be discussed using the characteristic approach. Other various generalizations of LLT will be pointed out. Finally, a concise combinatorial approach for LLT of simple random walk will be sketched. Time permits, I will talk about the generalized Berry-Esseen Inequality.

Thursday, April 18, 2019

2:00 pm in 347 Altgeld Hall,Thursday, April 18, 2019

#### Local Limit Theorem (Part 2)

###### Qiang Wu (UIUC Math)

Abstract: This talk the second part of an introduction to some classical CLT variants, specifically on local limit theorem (LLT). The proof of classical LLT for lattice and non-lattice distribution will be discussed using the characteristic approach. Other various generalizations of LLT will be pointed out. Finally, a concise combinatorial approach for LLT of simple random walk will be sketched. Time permits, I will talk about the generalized Berry-Esseen Inequality.

Thursday, April 25, 2019

2:00 pm in 347 Altgeld Hall,Thursday, April 25, 2019

#### Coupling and its applications

###### Peixue Wu (UIUC Math)

Abstract: I will define what is coupling. The beginning example is the transport problem, which leads to the concepts of optimal coupling and probability distance. We will also talk about applications of coupling to study ergodicity, gradient estimate and Harnack's inequality for Markov processes.