# Difference between revisions of "Probability Seminar"

(→Thursday, March 10, Jun Yin, UW-Madison) |
(→Thursday, January 28, Leonid Petrov, University of Virginia) |
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== Thursday, January 28, [http://faculty.virginia.edu/petrov/ Leonid Petrov], [http://www.math.virginia.edu/ University of Virginia] == | == Thursday, January 28, [http://faculty.virginia.edu/petrov/ Leonid Petrov], [http://www.math.virginia.edu/ University of Virginia] == | ||

− | + | Title: '''The quantum integrable particle system on the line''' | |

+ | |||

+ | I will discuss the higher spin six vertex model - an interacting particle | ||

+ | system on the discrete 1d line in the Kardar--Parisi--Zhang universality | ||

+ | class. Observables of this system admit explicit contour integral expressions | ||

+ | which degenerate to many known formulas of such type for other integrable | ||

+ | systems on the line in the KPZ class, including stochastic six vertex model, | ||

+ | ASEP, various $q$-TASEPs, and associated zero range processes. The structure | ||

+ | of the higher spin six vertex model (leading to contour integral formulas for | ||

+ | observables) is based on Cauchy summation identities for certain symmetric | ||

+ | rational functions, which in turn can be traced back to the sl2 Yang--Baxter | ||

+ | equation. This framework allows to also include space and spin inhomogeneities | ||

+ | into the picture, which leads to new particle systems with unusual phase | ||

+ | transitions. | ||

== Thursday, February 4, [http://homepages.math.uic.edu/~nenciu/Site/Contact.html Inina Nenciu], [http://www.math.uic.edu/ UIC] == | == Thursday, February 4, [http://homepages.math.uic.edu/~nenciu/Site/Contact.html Inina Nenciu], [http://www.math.uic.edu/ UIC] == |

## Revision as of 12:37, 20 January 2016

# Spring 2015

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

**
If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu.
**

## Thursday, January 28, Leonid Petrov, University of Virginia

Title: **The quantum integrable particle system on the line**

I will discuss the higher spin six vertex model - an interacting particle system on the discrete 1d line in the Kardar--Parisi--Zhang universality class. Observables of this system admit explicit contour integral expressions which degenerate to many known formulas of such type for other integrable systems on the line in the KPZ class, including stochastic six vertex model, ASEP, various $q$-TASEPs, and associated zero range processes. The structure of the higher spin six vertex model (leading to contour integral formulas for observables) is based on Cauchy summation identities for certain symmetric rational functions, which in turn can be traced back to the sl2 Yang--Baxter equation. This framework allows to also include space and spin inhomogeneities into the picture, which leads to new particle systems with unusual phase transitions.

## Thursday, February 4, Inina Nenciu, UIC

## Friday, February 5, Daniele Cappelletti speaks in the Applied Math Seminar, 2:25pm in Room 901

**Note:** Daniele Cappelletti is speaking in the Applied Math Seminar, but his research on stochastic reaction networks uses probability theory and is related to work of our own David Anderson.