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This graduate-level subject explores various mathematical aspects of (discrete) random walks and (continuum) diffusion.
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English [CC]
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Description
Applications include polymers, disordered media, turbulence, diffusion-limited aggregation, granular flow, and derivative securities.
Course content
- 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
Instructor
Massachusetts Institute of Technology
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