# Probability

Probability and Stochastic process is the study of randomness. It is at once a theoretical and abstract subject and one which is highly applied. Probability is both an increasingly core subject in mathematics and has long been an indispensable tool in applied modeling. Probability has been central in a number of recent Fields Medals. Probability is a required tool in topics ranging from modern population modeling to Bayesian statistics to phase transitions.

Probability at Duke spans from the ergodic theory of stochastic PDEs to waves through random media to random graphs and networks to cancer modeling.

## Faculty

#### Robert Calderbank

###### Charles S. Sydnor Professor of Computer Science

**Keywords in this area**

error-correcting codes, wireless communications, data storage, detection and estimation, algorithms, data compression, source classification

#### Rick Timothy Durrett

###### James B. Duke Professor of Mathematics

**Keywords in this area**

probability, stochastic processes, random graphs, dynamics on networks, dynamics of networks

#### Gregory Joseph Herschlag

###### Assistant Research Professor of Mathematics

**Keywords in this area**

kinetic equations, surface catalysis, molecular dynamics, stochastic boundary conditions

#### Jianfeng Lu

###### Associate Professor of Mathematics

**Keywords in this area**

rare events simulation, computational statistical mechanics, stochastic numerical methods

#### Mauro Maggioni

###### Research Professor of Mathematics

**Keywords in this area**

harmonic analysis, statistical learning, machine learning, signal processing, high-dimensional probability, stochastic dynamical systems, algorithms

#### Jonathan Christopher Mattingly

###### Professor of Mathematics

**Keywords in this area**

Stochastic and Random PDEs, Stochastic Dynamical Systems, Stochastic Analysis, Malliavin Calculus, Markov Chain Mixing, Ergodic Theory, High Dimensional Random Algorithms, Probability on stratified spaces, Out of equilibrium statistical mechanics, Approximating invariant measures

#### Sayan Mukherjee

###### Professor of Statistical Science

**Keywords in this area**

stochastic topology, Bayesian statistics, probability

#### James H. Nolen

###### Associate Professor of Mathematics

**Keywords in this area**

homogenization of partial differential equations, stochastic dynamical systems, random media, asymptotic analysis

#### Arlie O. Petters

###### Benjamin Powell Professor of Mathematics in Trinity College of Arts and Sciences

**Keywords in this area**

stochastic lensing, mathematical finance

#### Marc Daniel Ryser

###### Instructor in the Department of Population Health Sciences

**Keywords in this area**

cancer biology, cancer epidemiology, early carcinogenesis, Human papillomavirus, cancer evolution

#### Hau-Tieng Wu

###### Associate Professor of Mathematics

**Keywords in this area**

empirical process, large deviation theory