Website for:
Topics in Applied Stochastic Processes
and Topics in Discrete Probability

  • Week 1: January 6th.

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  • Topics Covered
    • From: Chapter 1 in [AHdHVvZ]
    • Finite-Length Random Walks on ${\mathbb Z}^d$

  • Week 2: January 13th.

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  • Topics Covered
    • Chapter 2 in [AHdHVvZ]
    • Infinite Length Random Walks on ${\mathbb Z}^d$

  • Week 3: January 20th.

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  • No class.
  • Topics Covered

  • Week 4: January 27th.

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  • Topics Covered
    • Random Walk on Graphs
    • Definition and Examples
    • Hitting Times

  • Week 5: February 3rd, 2023.

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  • Topics Covered
    • Transition Density
    • Laplacian
    • Dirichlet Form
    • Discrete Gauss-Green Theorem

  • Week 6: February 10th, 2023.

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  • Topics Covered
    • Local Central Theorem for Random walk on ${\mathbb Z}^d$

  • Week 7: February 17th, 2023.

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  • Topics Covered
    • Killed Transition Density
    • Green Function

  • February 24th, 2023.

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  • Topics Covered
    • Midterm

  • Week 8: March 3rd, 2023.

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  • Topics Covered
    • Harmonic Functions
    • Foster's Criterion
    • Louiville Property
    • Martingale Convergence Theorem

  • Week 9: March 10th, 2023.

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  • Topics Covered
    • Isoperimetric Inequality
    • Nash Inequality

  • Week 10: March 17th, 2023.

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  • Topics Covered
    • On Diagonal Heat Kernel Upper bounds.
    • Carne-Varapolous bounds.

  • Week 11: March 24th, 2023.

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  • Topics Covered
    • Large Deviation Principle for Random Walks.
    • Based on Chapter 1 from Large Deviations by Frank den Hollander

  • Week 12: March 31st, 2023.

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  • Topics Covered
    • Random Walks in a Field of Mobile Poisson Traps:- Model Definition
    • Pascal Principle (Lemma 2.2 in DGRS12)

  • Week 13: April 7th, 2023.

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  • Topics Covered
    • Holiday

  • Week 14: April 14th, 2023.

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  • Topics Covered
Last Modified: 2nd, February 2023. Courses Page Teaching Page