Pierre Patie

I am broadly interested in the study and applications of linear operators and related objects. This encompasses the following topics:

  Isospectral classes of linear operators: (pseudo-) unitary conjugation, Markov interwining, interweaving, gateway (duality) and weak similarity orbit
   ↬ Spectral and perturbation theory of (non)-selfadjoint operators
   ↬ Convergence to equilibrium, hypocoercivity, hyper(ultra)contractivity, cut-off phenomena
   ↬ Scaling limit and universality
   ↬ Representation theory and operator algebra

   Potential theory of Markov processes
   ↬ Martin boundary and exit problems for (non)-Markovian processes with jumps
   ↬ Boundary crossing problems
   ↬ Optimal stopping problems

  Computational mathematics

  Special topics:   Self-similar Markov processes,   Exponential functional of Lévy processes,   Subdiffusive processes,   The moment problem,   Special functions,   Asymptotic analysis,   Financial and insurance mathematics and Neurology

Publications

Full list of Publications and my ORCID iD icon

ORCID Profile

Submitted

Some recently published/accepted papers

Jacobi processes with jumps as neuronal models: a first passage time analysis with G. D'Onofrio and L. Sacerdote,
SIAM Journal on Applied Mathematics, 2023
Weak similarity orbit of (log)-self-similar semigroups in the Euclidean space with R. Sarkar
Proceedings of the London Mathematical Society, 2023
A new class of solutions to the van Dantzig problem, the Lee-Yang property and the Riemann hypothesis with T. Konstantopoulos and R. Sarkar
Annales de l'Institut Fourier, 2023
First passage times over stochastic boundaries for subdiffusive processes with C. Constantinescu and R.L. Loeffen
Transactions of the American Mathematical Society, 2022
Discrete self-similar and ergodic Markov chains with L. Miclo and R. Sarkar
Annals of Probability, 2022
Non-classical Tauberian and Abelian type criteria for the moment problem with A. Vaidyanathan
Mathematische Nachrichten, 2022
Spectral expansions of non-self-adjoint generalized Laguerre semigroups with M. Savov
Memoirs of the American Mathematical Society, 2021
On interweaving relations with L. Miclo
Journal of Functional Analysis, 2021
On non-local ergodic Jacobi semigroups: spectral theory, convergence-to-equilibrium and contractivity with P. Cheridito, A. Srapionyan and A. Vaidyanathan
Journal de l'Ecole Polytechnique - Mathématiques, 2021
Risk-neutral pricing techniques and examples with R. A. Jarrow, A. Srapionyan and Y. Zhao
Mathematical Finance, 2021
A spectral approach for hypocoercivity applied to some degenerate hypoelliptic, and non-local operators with with A. Vaidyanathan
Kinetic and Related Models, 2020
Intertwining, excursion theory and Krein theory of strings for non-self-adjoint Markov semigroups with M. Savov and Y. Zhao
Annals of Probability, 2019
Skip-free Markov chains with M.C.H. Choi
Transactions of the American Mathematical Society, 2019
Extinction time of non-Markovian self-similar processes, persistence, annihilation of jumps and the Fréchet distribution with R.L. Loeffen and M. Savov
Journal of Statistical Physics, 2019
On a gateway between continuous and discrete Bessel and Laguerre processes with L. Miclo
Annales Henri Lebesgue, 2019
Bernstein-gamma functions and exponential functionals of Lévy Processes with M. Savov
Electronic Journal of Probability, 2018
Cauchy problem of the non-self-adjoint Gauss-Laguerre semigroups and uniform bounds of generalized Laguerre polynomials with M. Savov
Journal of Spectral Theory, 2017
Boundary crossing identities for Brownian motion and some nonlinear ode's with L. Alili
Proceedings of American Mathematical Society, 2014
Law of the absorption time of positive self-similar Markov processes
Annals of Probability, 2012

List of co-authors: L. Alili, G. Ascione, F. Avram, C. Bartholmé, L. Chaumont, M. Chazal, A. Chee, P. Cheridito, M.C.H. Choi, M. Cissé, C. Constantinescu, G. D'Onofrio, P. Embrechts, R. Frey, X.Y. Han, B. Jarrow, R. Kaufmann, T. Konstantopoulos, A. Kyprianou, Y. Liu, R.L. Loeffen, L. Miclo, J.-C. Pardo, J.L. Pedersen, L. Sacerdote, R. Sarkar, M. Savov, T. Simon, A. Srapionyan, E. Tanré, T. Tian, B. Toaldo, A. Vaidyanathan, S. Vakeroudis, J. Wang, C . Winter, Y. Zhao

PhD Students

Here are the PhD students I have/had the chance to work with:

Filip Stojanovic (ORIE, Cornell), since 2023

Andrew Chee (ORIE, Cornell), 2023
Algebraic, analytical and numerical perspectives on the universe of integrable systems
Rohan Sarkar (ORIE, Cornell), 2021
Continuous and discrete self-similarity via classification schemes of Markov processes, and the van Dantzig problem
Jian Wang (ORIE, Cornell), 2020
Continuous time skip-free Markov process and study of branching process with immigration
Aditya Vaidyanathan (CAM, Cornell), 2019
Contributions to the Stieltjes moment problems and to the intertwining of Markov semigroups
Anna Srapyonian (CAM, Cornell), 2019
Some spectral ideas applied to finance and to self-similar and long-range dependent processes
Michael C.H. Choi (ORIE, Cornell), 2017
Analysis of non-reversible Markov chains
Yixuan Zhao (ORIE, Cornell), 2017
Spectral expansions and excursion theory for non-self-adjoint Markov semigroups with applications in mathematical finance
Christopher Van Weverberg (ULB), co-supervised with G. Deelstra, 2015
Contributions to the study of affine processes with applications in insurance
Carine Bartholmé (ULB), 2014
Self-similarity and exponential functionals of Lévy processes

Seminars

Intertwining between Probability, Analysis and Statistical Physics, IMS Workshop, Singapore, 05-15th Aug 2024