# Difference between revisions of "Probability Seminar"

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== Thursday, 1/26/2017, [http://mathematics.stanford.edu/people/name/erik-bates/ Erik Bates], [http://mathematics.stanford.edu/ Stanford] == | == Thursday, 1/26/2017, [http://mathematics.stanford.edu/people/name/erik-bates/ Erik Bates], [http://mathematics.stanford.edu/ Stanford] == | ||

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+ | Title: '''The endpoint distribution of directed polymers''' | ||

+ | |||

+ | Abstract: On the d-dimensional integer lattice, directed polymers are paths of a random walk in random environment, except that the environment updates at each time step. The result is a statistical mechanical system, whose qualitative behavior is governed by a temperature parameter and the law of the environment. Historically, the phase transitions have been best understood by whether or not the path’s endpoint localizes. While the endpoint is no longer a Markov process as in a random walk, its quenched distribution is. The key difficulty is that the space of measures is too large for one to expect convergence results. By adapting methods recently used by Mukherjee and Varadhan, we develop a compactification theory to resolve the issue. In this talk, we will discuss this intriguing abstraction, as well as new concrete theorems it allows us to prove for directed polymers. | ||

+ | This talk is based on joint work with Sourav Chatterjee. | ||

+ | |||

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## Revision as of 14:20, 20 January 2017

# Spring 2017

**Thursdays in 901 Van Vleck Hall at 2:25 PM**, unless otherwise noted.
**We usually end for questions at 3:15 PM.**

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.

## Monday, January 9, 4pm, B233 Van Vleck Miklos Racz, Microsoft Research

** Please note the unusual day and time **

Title: **Statistical inference in networks and genomics**

Abstract:
From networks to genomics, large amounts of data are increasingly available and play critical roles in helping us understand complex systems. Statistical inference is crucial in discovering the underlying structures present in these systems, whether this concerns the time evolution of a network, an underlying geometric structure, or reconstructing a DNA sequence from partial and noisy information. In this talk I will discuss several fundamental detection and estimation problems in these areas.

I will present an overview of recent developments in source detection and estimation in randomly growing graphs. For example, can one detect the influence of the initial seed graph? How good are root-finding algorithms? I will also discuss inference in random geometric graphs: can one detect and estimate an underlying high-dimensional geometric structure? Finally, I will discuss statistical error correction algorithms for DNA sequencing that are motivated by DNA storage, which aims to use synthetic DNA as a high-density, durable, and easy-to-manipulate storage medium of digital data.

## Thursday, 1/26/2017, Erik Bates, Stanford

Title: **The endpoint distribution of directed polymers**

Abstract: On the d-dimensional integer lattice, directed polymers are paths of a random walk in random environment, except that the environment updates at each time step. The result is a statistical mechanical system, whose qualitative behavior is governed by a temperature parameter and the law of the environment. Historically, the phase transitions have been best understood by whether or not the path’s endpoint localizes. While the endpoint is no longer a Markov process as in a random walk, its quenched distribution is. The key difficulty is that the space of measures is too large for one to expect convergence results. By adapting methods recently used by Mukherjee and Varadhan, we develop a compactification theory to resolve the issue. In this talk, we will discuss this intriguing abstraction, as well as new concrete theorems it allows us to prove for directed polymers. This talk is based on joint work with Sourav Chatterjee.