Statistics and Probability Seminars

Probability Seminar

Topic: 
Upper tails and independence polynomials in sparse random graphs
Abstract / Description: 

The upper tail problem in the Erd˝os–R´enyi random graph G ∼ Gn,p is to estimate the probability that the number of copies of a graph H in G exceeds its expectation by a factor 1 + δ. Already, for the case of triangles, the order in the exponent of the tail probability was a long-standing open problem until fairly recently, when it was solved by Chatterjee (2012), and independently by DeMarco and Kahn (2012). Recently, Chatterjee and Dembo (2014) showed that in the sparse regime, the logarithm of the tail probability reduces to a natural variational problem on the space of weighted graphs. In this talk we derive the exact asymptotics of the tail probability by solving this variational problem for any fixed graph H. As it turns out, the leading order constant in the large deviation rate function is governed by the independence polynomial of H.


This is based on joint work with Shirshendu Ganguly, Eyal Lubetzky, and Yufei Zhao.


 

The Probability Seminars are held in Sequoia Hall, Room 200, at 4:30pm on Mondays. Refreshments are served at 4pm in the Lounge on the first floor.

Date and Time: 
Monday, January 11, 2016 - 4:30pm to 5:30pm
Venue: 
Sequoia Hall, Room 200

Probability Seminar

Topic: 
The Yang–Mills free energy
Abstract / Description: 

The construction of four-dimensional quantum Yang–Mills theories is a central open question in mathematical physics, famously posed as one of the millennium prize problems by the Clay Institute. While much progress has been made for the two dimensional problem, the techniques mostly break down in dimensions three and four. In this talk I will present a partial advance on this question, taking the program one step beyond the results proved in the Eighties.


 

The Probability Seminars are held in Sequoia Hall, Room 200, at 4:30pm on Mondays. Refreshments are served at 4pm in the Lounge on the first floor.

Date and Time: 
Monday, January 25, 2016 - 4:30pm to 5:30pm
Venue: 
Sequoia Hall, Room 200

Probability Seminar

Topic: 
Limit behavior of some Pólya urn models associated to preferential attachment graphs and random trees
Abstract / Description: 

The Probability Seminars are held in Sequoia Hall, Room 200, at 4:30pm on Mondays. Refreshments are served at 4pm in the Lounge on the first floor.

Date and Time: 
Monday, January 4, 2016 - 4:30pm to 5:30pm
Venue: 
Sequoia Hall, Room 200

Probability Special Seminar

Topic: 
Siegmund duality for Markov chains on partially ordered state spaces: Generalized Gambler's Ruin problem
Abstract / Description: 

Special Probability Seminar are held in Sequoia Hall, Room 200, at 4:30pm.

Refreshments are served at 4pm in the Lounge on the first floor.

Date and Time: 
Wednesday, January 6, 2016 - 4:30pm to 5:30pm
Venue: 
Sequoia Hall, Room 200

Statistics Seminar: A Special Event

Topic: 
A Celebration in Honor of Ingram Olkin on his 90th Birthday
Abstract / Description: 

A Special Event hosted by Stanford Statistics

  • 2:20pm Guenther Walther, Statistics Department Chair Welcome and Opening Remarks
  • 2:30pm Michael Perlman, University of Washington "Olkin's STAT 384: Fifty Years of Inspiration"
  • 3pm Albert W. Marshall, University of British Columbia "57 Years of Collaboration"
  • 3:30pm Break
  • 4pm Larry V. Hedges, Northwestern University "The Development of Meta-Analysis"
  • 4:30pm Betsy B. Becker, Florida State University "The Olkin Legacy in Three Domains"
Date and Time: 
Tuesday, November 10, 2015 - 2:00pm to 4:30pm
Venue: 
LKSC Berg C

Statistics Seminar

Topic: 
Sparse Inverse Problems
Abstract / Description: 

We present an efficient algorithm and theoretical analysis for an infinite-dimensional analogue of the Lasso. 

Compressed sensing seeks to explain an observed signal as the noisy measurement of a few weighted sources. Identifying a weighted collection of parametric sources with a measure on the parameter space allows one to estimate the underlying sources using an infinitedimensional analogue of the Lasso. In many applications the mapping from parameters to observations is differentiable; we propose an algorithm and theoretical analysis that leverages structure in the measurement mapping. 

We propose an algorithm that interleaves conditional gradient steps on the infinite-dimensional Lasso with nonconvex local search over the parameter space. We outline applications of our algorithm to super-resolution imaging, low-rank matrix completion, linear system identification, and radiation treatment planning. 

We prove that in ideal settings the optimization problem recovers the true parameters. Precisely, we restrict our theoretical analysis to the setting with a one-dimensional parameter space, positive weights, and noiseless observations. We establish conditions on the measurement function such that minimizing the weighted total variation recovers the true parameters and weights, with no minimum separation condition on the source locations

Date and Time: 
Tuesday, October 27, 2015 - 4:30pm to 5:30pm
Venue: 
Sequoia Hall, Room 200

Probability Seminar

Topic: 
Winding of planar stationary Gaussian processes
Abstract / Description: 

Consider random stationary complex-valued Gaussian functions defined on the real axis. That is, random paths, invariant under time-shifts, whose finite marginals are (centered) Gaussian. Such processes are used by physicists to model objects such as polymers and random flux lines of magnetic fields. The winding number of the process on a large interval represents the "entanglement" of the polymer or the flux line in space.


In this talk, we explain how to use elementary complex and harmonic analysis, combined with well-known Gaussian properties, in order to obtain exact formulae for the mean and variance of this quantity, and prove a central limit theorem. In doing so, we give rigorous proofs to predictions by physicists (e.g., Le Doussal–Etzioni–Horovitz). The talk will be self-contained, with special emphasis given to tools which may find applications elsewhere.

This is joint work with Jeremiah Buckley.

 


The Probability Seminars are held in Sequoia Hall, Room 200, at 4:30pm on Mondays. Refreshments are served at 4pm in the Lounge on the first floor.

Date and Time: 
Monday, September 28, 2015 - 4:30pm to 5:30pm
Venue: 
Sequoia Hall, Room 200

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