Probability

Members of the Group

Nizar Bou Ezz, Graduate Student
Lancelot Leung, Graduate Student
Luke Peilen, Research Assistant Professor
Silvana Ramaj, Graduate Student
Brian Rider, Professor, Department Chair
Wei-Shih Yang, Professor
Atilla Yilmaz, Associate Professor

Members of the Probability Group do research on a wide range of topics in probability theory, stochastic processes and their applications. They have natural connections to the Analysis Group, especially through partial differential equations. They work mainly on various models that have originated in mathematical physics, and also on problems coming from biology, computer science, information theory and operations research. Their areas of expertise include:

Complex networks
Determinantal point processes
Large deviations
Processes in random environments
Quantum computing
Quantum random walks
Random matrix theory
Random Schroedinger operators
Statistical mechanics
Stochastic homogenization
Stochastic optimal control
Stochastic population dynamics

There is a weekly Probability Seminar (the link to the external website will appear) organized jointly by Temple University and the University of Pennsylvania. It allows interested faculty members, postdocs and graduate students from all the universities in the Philadelphia area to be informed about the cutting-edge developments in the field as well as to regularly interact with each other.

The Probability Group participates in the organization of the Northeast Probability Seminar, which is a high-profile annual meeting in the region. Members of the group also take advantage of Philadelphia's superb location and attend conferences, seminars and workshops organized by nearby universities and institutes.

Selected Courses:

Math 5032: Stochastic Calculus

In this course, we introduce the theory of Ito calculus and stochastic differential equations based on Brownian motion and Gaussian processes (avoiding the subtleties of measure and integration whenever possible), illustrate the concepts and results with concrete examples and numerical projects, and present some of the fundamental applications of the theory to option pricing in finance.

Math 5034: High-dimensional Probability

This course provides a self-contained introduction to the area of high-dimensional probability and statistics from a non-asymptotic perspective, aimed at students across the mathematical sciences. It includes a focus on core methodology and theory (tail bounds, concentration of measure, random matrices, random graphs and networks) as well as in-depth exploration of various applications (to statistical learning theory, sparse linear and graphical models, community detection, as examples).

Math 8031: Probability Theory

In this course, we introduce the axioms and fundamental notions of probability based on measure and integration, develop the theory with the accompanying probabilistic intuition which is equally important, formulate and prove the strong law of large numbers for independent random variables, define and characterize weak convergence of probability measures, and give a rigorous treatment of the central limit theorem.

Math 8032: Stochastic Processes

Department of Mathematics

Probability

Selected Courses:

Go back to Department of Mathematics More in Research

Department of Mathematics

Selected Courses:

Go back to Department of MathematicsMore in Research

Go back to Department of Mathematics More in Research