Books, Lecture Notes, Review Articles, and Proceedings:
- with M. Damron and
T. Seppäläinen (Editors): Random Growth Models. Proceedings of Symposia in Applied Mathematics, 75, American Mathematical Society, Providence. (2018) (Front matter) (Index)
(on Amazon) (on Google)
- with
M. Damron and
T. Seppäläinen:
Random growth models.
Notices of the AMS, 63, 1004-1008. (2016)
- with
M. Damron and
T. Seppäläinen:
AMS short course in Atlanta, GA.
Notices of the AMS, 63, 1087-1090. (2016)
- Videos of a full first-semester course on graduate (measure theoretic) probability are available here.
- with
D. Khoshnevisan:
Introduction to probability.
These are the lecture notes I use for undergraduate probability. Full video lectures are also available here.
- with
T. Seppäläinen:
A course on large deviations with an introduction to Gibbs measures.
Graduate Studies in Mathematics, 162, American Mathematical Society, Providence. (2015)
(on Amazon) (on Google)
(Errata)
- with D. Khoshnevisan (Editors):
A Minicourse on Stochastic Partial Differential Equations.
Lect. Notes in Math, 1962, Springer-Verlag, Berlin (2009); Authors: R. Dalang, D. Khoshnevisan, C. Mueller, D. Nualart, and Y. Xiao.
(on Amazon)
Articles Submitted for Publication:
- with
S. Groathouse,
T. Seppäläinen, and
E. Sorensen:
Jointly invariant measures for the Kardar-Parisi-Zhang equation.
(2023)
- with
S. Groathouse and
C. Janjigian:
Existence of generalized Busemann functions and Gibbs measures for random walks in random potentials.
(2023)
- with
C. Janjigian
and T. Seppäläinen:
Ergodicity and synchronization of the Kardar-Parisi-Zhang equation.
(2022)
- with
T. Alberts,
C. Janjigian,
and T. Seppäläinen:
The Green’s function of the parabolic Anderson model
and the continuum directed polymer.
(2022)
- with
S. Groathouse and
C. Janjigian:
Non-existence of non-trivial bi-infinite geodesics in Geometric last passage percolation.
(2021)
Articles in Refereed Journals:
- with
T. Seppäläinen
and X. Shen:
Coalescence and total-variation distance of semi-infinite inverse-gamma polymers.
J. London Math. Soc., To appear (2024)
- with
A. Krishnan and
T. Seppäläinen:
Geodesic length and shifted weights in first-passage percolation.
Comm. Amer. Math. Soc., 3, 209-289 (2023)
[Talk at Probability and the City]
- with
C. Janjigian and
T. Seppäläinen:
Geometry of geodesics through Busemann measures in directed last-passage percolation.
J. Eur. Math. Soc., 25, 2573–2639
(2023) [Talk at IPAM]
[Talk at MSRI]
- with
C. Janjigian and
S. Nurbavliyev:
A shape theorem and a variational formula for the quenched Lyapunov exponent of random walk in a random potential.
Ann. Inst. H. Poincaré Probab. Statist., 58, 1010-1040 (2022)
- with
C. Janjigian:
Uniqueness and ergodicity of stationary directed polymer models on the square lattice.
J. Stat. Phys., 179, 672–689 (2020)
- with
T. Alberts and
M. Simper:
Busemann functions and semi-infinite O'Connell-Yor polymers.
Bernoulli., 26, 1927-1955. (2020)
- with
C. Janjigian:
Busemann functions and Gibbs measures in directed polymer models on \(\mathbb{Z}^2\).
Ann. Probab., 48, 778-816. (2020)
- with
M. Balázs and
T. Seppäläinen:
Large deviations and wandering exponent for random walk in a dynamic beta environment.
Ann. Probab., 47, 2186-2229. (2019)
- with
M. Joseph and
T. Seppäläinen:
Independent particles in a dynamical random environment. In: Friz P., König W., Mukherjee C., Olla S. (eds)
Probability and Analysis in Interacting Physical Systems. VAR75 2016. Springer Proceedings in Mathematics & Statistics, 283, 75-121. Springer, Cham. Special Proceedings Volume in honor of Raghu Varadhan's 75th birthday. (2019)
- with
K. Smith and
C. Strong:
Multisite generalization of the SHArP weather generator.
J. Appl. Meteor. Climatol., 57, 2113-2127. (2018)
- with
N. Georgiou and
T. Seppäläinen:
Geodesics and the competition interface for the corner growth model.
Probab. Th. Rel. Fields, 169, 223-255. (2017)
- with
N. Georgiou and
T. Seppäläinen:
Stationary cocycles and Busemann functions for the corner growth model.
Probab. Th. Rel. Fields, 169, 177-222. (2017)
- with
T. Seppäläinen and
A. Yilmaz:
Averaged vs. quenched large deviations and entropy for random walk in a dynamic random environment. Electron. J. Probab., 22, 1-47. (2017)
- with
K. Smith and
C. Strong:
A new method for generating stochastic simulations of air temperature.
J. Appl. Meteor. Climatol., 56, 953-963. (2017)
- with
T. Seppäläinen and
A. Yilmaz:
Variational formulas and disorder regimes of random walks in random potentials. Bernoulli, 23, 405-431. (2017)
- with
N. Georgiou and
T. Seppäläinen:
Variational formulas and cocycle solutions for directed polymer and percolation models.
Commun. Math. Phys., 346, 741-779. (2016)
- with
N. Georgiou,
T. Seppäläinen and
A. Yilmaz:
Ratios of partition functions for the log-gamma polymer.
Ann. Probab., 43, 2282-2331. (2015)
- with
A. Borisyuk:
Quasiperiodicity and phase locking in stochastic circle maps:
a spectral approach.
Phys. D: Nonlinear Phenomena, 288, 30-44. (2014)
[Preprint with videos embedded (larger file)]
[Videos]
- with
T. Seppäläinen:
Quenched point-to-point free energy for random walks in random potentials.
Probab. Th. Rel. Fields, 158, 711-750. (2014)
- with
D. Campos,
A. Drewitz,
A.F. Ramírez, and
T. Seppäläinen:
Level 1 quenched large deviation principle for random walk in dynamic
random environment.
Bull. Inst. Math. Acad. Sin., 8, 1-29. Special Issue in honor of the
70th birthday of Raghu Varadhan. (2013)
- with
T. Seppäläinen and
A. Yilmaz:
Quenched free energy and large deviations for random walks in random potentials.
Comm. Pure Appl. Math., 66, 202-244. (2013)
- with
M. Joseph:
Almost sure invariance principle for continuous space random walk in dynamic random environment.
ALEA Lat. Am. J. Probab. Math. Stat., 8, 43-57. (2011)
- with
T. Seppäläinen:
Process-level quenched large deviations for random walk in random environment.
Ann. Inst. H. Poincaré Probab. Statist., 47, 214-242. (2011)
- with
T. Seppäläinen:
Almost sure functional central limit theorem for ballistic
random walk in random environment.
Ann. Inst. H. Poincaré Probab. Statist., 45, 373-420. (2009)
- with
T. Seppäläinen:
An almost sure invariance principle for additive functionals of Markov
chains.
Statist. Probab. Lett., 78, 854-860. (2008)
- with
M. Balázs,
T. Seppäläinen, and
S. Sethuraman:
Existence of the zero range process and a deposition model with
superlinear growth rates.
Ann. Probab., 35, 1209-1249. (2007)
- with
T. Seppäläinen:
Quenched invariance principle for multidimensional ballistic random walk in
a random environment with a forbidden direction.
Ann. Probab., 35, 1-31. (2007)
- with
M. Balázs and
T. Seppäläinen:
The random average process and random walk in
a space-time random environment in one dimension.
Commun. Math. Phys., 266, 499-545. (2006)
- with
T. Seppäläinen:
Ballistic random walk in a random environment with a forbidden direction.
ALEA Lat. Am. J. Probab. Math. Stat., 1, 111-147. (2006)
- with
T. Seppäläinen:
An almost sure invariance principle for random walks in a space-time
random environment.
Probab. Th. Rel. Fields, 133, 299-314. (2005)
-
On the zero-one law and the law of large numbers for a random walk in a mixing
random environment.
Electron. Comm. in Probab. 10, 36-44. (2005)
-
Large deviations for random walks in a mixing random environment
and other (non-Markov) random walks.
Comm. Pure Appl. Math. 57, 1178-1196. (2004)
-
The point of view of the particle on the law of large numbers for
random walks in a mixing random environment.
Ann. Probab. 31, 1441-1463. (2003)
Preprints and Extended Versions:
- with
C. Janjigian:
Busemann functions and Gibbs measures in directed polymer models on \(\mathbb{Z}^2\).
Extended version (includes a coalescence appendix). (2018)
- with
M. Balázs and
T. Seppäläinen:
Wandering exponent and large deviations for random walk in a dynamic beta environment. Extended version.
(2018)
- with
N. Georgiou and
T. Seppäläinen:
Geodesics and the competition interface for the corner growth model. Extended version (includes a coalescence appendix).
(2015)
- with
N. Georgiou and
T. Seppäläinen:
Stationary cocycles for the corner growth model. Extended Version.
(2015)
- with
T. Seppäläinen:
Quenched point-to-point free energy for random walks in random potentials.
Extended Version. (2012)
- with
T. Seppäläinen:
Almost sure functional central limit theorem for non-nestling
random walk in random environment.
Preprint. (2007)
-
Le comportement non-récurrent dans la dynamique quantique:
Le rotateur quantique.
Preprints of the University of Paris 7 (1996)
(English abstract)
