MATH 289A: TOPICS IN PROBABILITY (FALL 2008)
  • Lecture 1-2: Introduction
  • Lectures 3-5: Path Space, Weak Convergence of Stochastic Processes
  • Lecture 4: Notes from October 20, 2008, taken by Allison Cuttler.
  • Lecture 5: Notes from October 22, 2008, taken by Feng Liu.
  • Lecture 6: Start of Biochemical Reaction Networks -- notes from October 27, 2008, taken by Chris Chang.
  • Lecture 7: Fluid limits of Biochemical reaction networks -- notes from October 29, 2008, taken by Alex Bilik. Beware, this is a large file (in megabytes). A typed verson of the notes is available here.
  • Lecture 8: Fluid limit justification with mass action kinetics -- notes from November 3, 2008, taken by Michael Kinnally.
  • Lecture 9: Counting Equilibria for Fluid Limit Models. For notes from November 5, 2008, taken by Wen Chen, click here. A pdf file of some slides for the lecture is here. For the related paper by Craciun, Helton and Williams, click here.
  • Lecture 10: Complex balance equilibrium. For notes taken by Bo Hu on November 10, 2008, click here. (Decomposition of RHS of ode in form YA Psi. For a mathematica notebook to do this automatically, click here.)
  • Lecture 11: Complex balance and connection to product form stationary distributions, November 12, 2008. For the paper of Anderson, Craciun and Kurtz, click here. For notes taken by Raghava Swamy, click here.
  • Lecture 12: Completion of proof of product form solutions from complex balance solutions and start of diffusion approximations for biochemical reaction networks, November 17, 2008. Click here for notes taken by Minghui Zhu.
  • Lecture 13: Continuation of Van Kampen and Langevin diffusion approximations for biochemical reaction networks, November 19, 2008. For Teng Gao's notes, click here.
  • Lecture 14: November 24, 2008. Single class queueing networks: setup and fluid models. Click here for notes taken by Vladimir Pesic.
  • Lecture 15: November 26, 2008. Stability of fluid model solutions under nominal conditions. For notes by Mike Scullard, click here.
  • Lecture 16: December 1, 2008. For notes by Abhijeet Bhorkar, click here.
  • Lecture 17: December 3, 2008. Overview of stability and heavy traffic diffusion approximations for multiclass queueing networks. Click here for slides from this lecture.
  • Schedule of Presentations by Students.
    1. Skorokhod Representation Theorem: Allison Cuttler, Friday, October 31, noon-12.50pm.
    For Allison's notes, click here. Some notes on the web by Borkar relating to the Skorokhod space.
    2. Central limit theorem for heavy tails: Alex Bilik, and Chris Chang, Friday, November 14, 2008, noon-12.50p.m. Some slides from Chris Chang's presentation.
    3. Ode models in biochemistry: Bo Hu and Wen Chen, November 21, 2008, noon-1pm. For publications related to Bo Hu's presentation on yeast MAPK signalling specificity, click here and here for supporting material.
    4. Skorokhod problem: Teng Gao, November 21, 2008, 1-1.30pm
    5. Reversibility: Michael Scullard, December 5, 2008, noon-12.30pm.
    6. M1 topology: Michael Kinnally; December 5, 2008,12.30pm-1pm
    7. Diffusion approximation for a two-user downlink system in heavy traffic: Raghava Swamy, December 5, 2008, 1pm-1.30pm.
    8. Stolyar's maxweight paper: Abhijeet Bhorkar, probably December 5, 2008, 3.30-4pm, AP&M 7421.
    9. Strong approximations for Markovian service systems: Vladimir Pesic and Ming Hui, December 5, 2008, 4pm-5pm, AP&M 7421.