MATH 232: Topics in Probability: Percolation Theory
An introduction to first passage percolation and related general tools and models. Topics include early results on shape theorems and fluctuations, more modern development using hypercontractivity, recent breakthrough regarding scaling exponents, and providing exposure to some fundamental longstanding open problems. Course prerequisite: graduatelevel probability.
Terms: Aut

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Basu, R. (PI)
MATH 233A: Topics in Combinatorics
Terms: not given next year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 233B: Topics in Combinatorics: Polyhedral Techniques in Optimization
LP duality and minmax formulas; matchings, spanning trees, matroids, matroid union and intersection; packing of trees and arborescences; submodular functions, continuous extensions and optimization.
Terms: Win

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Vondrak, J. (PI)
MATH 233C: Topics in Combinatorics
Terms: Spr

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Fox, J. (PI)
MATH 234: Large Deviations Theory (STATS 374)
Combinatorial estimates and the method of types. Large deviation probabilities for partial sums and for empirical distributions, Cramer's and Sanov's theorems and their Markov extensions. Applications in statistics, information theory, and statistical mechanics. Prerequisite:
MATH 230A or
STATS 310. Offered every 23 years.
http://statweb.stanford.edu/~adembo/largedeviations/
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Dembo, A. (PI)
MATH 235A: Topics in combinatorics
This advanced course in extremal combinatorics covers several major themes in the area. These include extremal combinatorics and Ramsey theory, the graph regularity method, and algebraic methods.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 235B: Modern Markov Chain Theory
This is a graduatelevel course on the use and analysis of Markov chains. Emphasis is placed on explicit rates of convergence for chains used in applications to physics, biology, and statistics. Topics covered: basic constructions (metropolis, Gibbs sampler, data augmentation, hybrid Monte Carlo); spectral techniques (explicit diagonalization, Poincaré, and Cheeger bounds); functional inequalities (Nash, Sobolev, Log Sobolev); probabilistic techniques (coupling, stationary times, Harris recurrence). A variety of card shuffling processes will be studies. Central Limit and concentration.
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 235C: Topics in Markov Chains
Classical functional inequalities (Nash, FaberKrahn, logSobolev inequalities), comparison of Dirichlet forms. Random walks and isoperimetry of amenable groups (with a focus on solvable groups). Entropy, harmonic functions, and Poisson boundary (following KaimanovichVershik theory).
Terms: not given this year

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MATH 236: Introduction to Stochastic Differential Equations
Brownian motion, stochastic integrals, and diffusions as solutions of stochastic differential equations. Functionals of diffusions and their connection with partial differential equations. Random walk approximation of diffusions. Prerequisite: 136 or equivalent and differential equations.
Terms: Win

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Papanicolaou, G. (PI)
;
Chen, L. (TA)
MATH 237: Default and Systemic Risk
Introduction to mathematical models of complex static and dynamic stochastic systems that undergo sudden regime change in response to small changes in parameters. Examples from materials science (phase transitions), power grid models, financial and banking systems. Special emphasis on mean field models and their large deviations, including computational issues. Dynamic network models of financial systems and their stability.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
Filter Results: