Khoshnevisan’s research in probability theory spans three sub-concentrations: mathematical statistics, multi-parameter random processes, and stochastic partial differential equations. These topics are mathematically sophisticated yet have immediate applicability in engineering and applied sciences. His work in mathematical statistics is used in high dimensional data analysis, while his research in stochastic partial differential equations has been used to model the intermittency properties of sunspot phenomena over time. His work on multi-parameter random processes led to the resolution of several long-standing conjectures on fractal properties of random fields, some of which dated back to the 1930s.
A prolific author of over 135 research papers that have been cited over 1,800 times, fully one-quarter of Khoshnevisan’s articles have appeared in Annals of Probability or Probability Theory and Related Fields, the most well-regarded journals in the field.
Additionally, Khoshnevisan is known as an excellent expositor. His textbook Probability is used in graduate-level probability courses across the country, and his monograph Multiparameter Processes is the standard in the field. His upcoming book Gaussian Analysis is intended for beginning researchers. He has also served in an editorial role for several prestigious journals.
Related to his publications, Khoshnevisan has received numerous accolades in recognition of his prodigious research output and his professional service, including in 1998 the Rollo Davidson prize. In 2015 he was made a Fellow of the Institute of Mathematical Statistics, and in 2020 he was elected as a Fellow of the American Mathematical Society. Then, in 2018 he was recognized as a Medallion Lecturer at the Institute of Mathematical Statistics’ annual conference.
Of special note is Khoshnevisan’s mentorship of young mathematicians. At least 50 of his research articles are jointly authored with his postdoctoral fellows and graduate students. At the U, Khoshnevisan has directly supervised 14 postdoctoral fellows, 10 PhD students, and nine master's of statistics students.
Khoshnevisan has been continuously funded by the National Science Foundation since 1997, with his most recent grant extending into 2026. This is a remarkable achievement given the exponential increase in probability research during that period and is an extraordinary validation of his research program. Equally impressive is that he was able to maintain his research funding while taking on the additional responsibilities of department chair. In 2020 alone, while chair and managing the pandemic, he published five remarkable articles on spatial ergodicity of solutions to stochastic partial differential equations. Already this work is being recognized as fundamentally important in the field.
“I am thrilled that Davar Khoshnevisan has been selected as a Distinguished Professor for the 2023-24 academic year,” says Department Chair Tommaso de Fernex. “This is a great accomplishment and well deserved recognition.”
by Tom Alberts