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Last updated:

September 23, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion.

Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.

Course Curriculum

  • Overview Unlimited
  • Moments, Cumulants, and Scaling Unlimited
  • Multi-dimensional CLT for Ssums of IID Random Vectors Unlimited
  • Continuum Unlimited
  • Berry-Esseen Theorem Unlimited
  • Globally Valid Asymptotic Unlimited
  • Power-law Tails Unlimited
  • Asymptotics with Fat Tails Unlimited
  • From Random Walks to Diffusion Unlimited
  • Discrete Versus Continuous Stochastic Processes Unlimited
  • Weakly Non-identical Steps Unlimited
  • Nonlinear Drift Unlimited
  • Return Probability on a Lattice Unlimited
  • The Arcsine Distribution Unlimited
  • First Passage in the Continuum Limit Unlimited
  • First Passage in Arbitrary Geometries Unlimited
  • Conformal Invariance Unlimited
  • Hitting Probabilities in Two Dimensions Unlimited
  • Applications of Conformal Mapping Unlimited
  • Diffusion-limited Aggregation Unlimited
  • Polymer Models Unlimited
  • Levy Flights Unlimited
  • Continuous-time Random Walks Unlimited
  • Fractional Diffusion Equations Unlimited
  • Non-separable Continuous-time Random Walks Unlimited
  • Leapers and Creepers Unlimited

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Massachusetts Institute of Technology
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