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Probabilistic models of directed polymers in random environment have received considerable attention in recent years.
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Théorie de L’addition des Variables Aléatoires
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The concentration-compactness principle in the calculus of variations. The locally compact case. I
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The concentration-compactness principle in the calculus of variations. The locally compact case. II
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Pinning and roughening of domain walls in Ising systems due to random impurities
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The concentration-compactness principle in the calculus of variations. The limit case. I
Lions, P.-L · 1985
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Lions, P.-L · 1985
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Derrida, B., and Spohn, H · 1987
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Diffusion of directed polymers in a random environment
Imbrie, J. Z., and Spencer, T · 1988
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A note on the diffusion of directed polymers in a random environment
Bolthausen, E · 1989
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A remark concerning random walks with random potentials
Sinai, Y. G · 1995
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A martingale approach to directed polymers in a random environment
Albeverio, S., and Zhou, X. Y · 1996
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A remark on diffusion of directed polymers in random environments
Song, R., and Zhou, X. Y · 1996
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Weak convergence and empirical processes
van der Vaart, A. W., and Wellner, J. A · 1996
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The Burgers equation with a random force and a general model for directed polymers in random environments
Kifer, Y · 1997
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Directed polymers in a random environment: some results on fluctuations
Piza, M. S. T · 1997
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On the stability of the quenched state in mean-field spin-glass models
Aizenman, M., and Contucci, P · 1998
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A course on Borel sets
Srivastava, S. M · 1998
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Superdiffusive behavior of two-dimensional Brownian motion in a Poissonian potential
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Convergence of probability measures
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Shape fluctuations and random matrices
Johansson, K · 2000
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Topology
Munkres, J. R · 2000
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Superdiffusivity of polymers in random environment
Petermann, M · 2000
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Ordered overlaps in disordered mean-field models
Comets, F., and Dembo, A · 2001
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Brownian analogues of Burke’s theorem
O’Connell, N., and Yor, M · 2001
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On the partition function of a directed polymer in a Gaussian random environment
Carmona, P., and Hu, Y · 2002
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Directed polymers in a random environment: path localization and strong disorder
Comets, F., Shiga, T., and Yoshida, N · 2003
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Discrete polynuclear growth and determinantal processes
Johansson, K · 2003
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Random matrices, non-colliding processes and queues
O’Connell, N · 2003
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Probabilistic analysis of directed polymers in a random environment: a review
Comets, F., Shiga, T., and Yoshida, N · 2004
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Scaling for a one-dimensional directed polymer with boundary conditions
Seppäläinen, T · 2012
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Random overlap structures: properties and applications to spin glasses
Arguin, L.-P., and Chatterjee, S · 2013
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Log-gamma polymer free energy fluctuations via a Fredholm determinant identity
Borodin, A., Corwin, I., and Remenik, D · 2013
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Tail decay for the distribution of the endpoint of a directed polymer
Bothner, T., and Liechty, K · 2013
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Large deviation rate functions for the partition function in a log-gamma distributed random potential
Georgiou, N., and Seppäläinen, T · 2013
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Endpoint distribution of directed polymers in 1 + 1 1+1 dimensions
Moreno Flores, G., Quastel, J., and Remenik, D · 2013
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Some new results on Brownian directed polymers in random environment
Comets, F., and Yoshida, N · 2004
Cited alongside, same era.
Upper bound of a volume exponent for directed polymers in a random environment
Mejane, O · 2004
Cited alongside, same era.
A survey of max-type recursive distributional equations
Aldous, D. J., and Bandyopadhyay, A · 2005
Cited alongside, same era.
Brownian directed polymers in random environment
Comets, F., and Yoshida, N · 2005
Cited alongside, same era.
Characterization of invariant measures at the leading edge for competing particle systems
Ruzmaikina, A., and Aizenman, M · 2005
Cited alongside, same era.
Strong disorder implies strong localization for directed polymers in a random environment
Carmona, P., and Hu, Y · 2006
Cited alongside, same era.
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The Sherrington-Kirkpatrick model
Panchenko, D · 2013
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Quenched free energy and large deviations for random walks in random potentials
Rassoul-Agha, F., Seppäläinen, T., and Yilmaz, A · 2013
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The intermediate disorder regime for directed polymers in dimension 1 + 1 1+1
Alberts, T., Khanin, K., and Quastel, J · 2014
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Macdonald processes
Borodin, A., and Corwin, I · 2014
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Free energy fluctuations for directed polymers in random media in 1 + 1 1+1 dimension
Borodin, A., Corwin, I., and Ferrari, P · 2014
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Integrable probability: from representation theory to Macdonald processes
Borodin, A., and Petrov, L · 2014
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Tropical combinatorics and Whittaker functions
Corwin, I., O’Connell, N., Seppäläinen, T., and Zygouras, N · 2014
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Airy processes and variational problems
Quastel, J., and Remenik, D · 2014
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The strict-weak lattice polymer
Corwin, I., Seppäläinen, T., and Shen, H · 2015
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Ratios of partition functions for the log-gamma polymer
Georgiou, N., Rassoul-Agha, F., Seppäläinen, T., and Yilmaz, A · 2015
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Tails of the endpoint distribution of directed polymers
Quastel, J., and Remenik, D · 2015
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On integrable directed polymer models on the square lattice
Thiery, T., and Le Doussal, P · 2015
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Directed polymers in random environments
Comets, F · 2016
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Localization in log-gamma polymers with boundaries
Comets, F., and Nguyen, V.-L · 2016
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Variational formulas and cocycle solutions for directed polymer and percolation models
Georgiou, N., Rassoul-Agha, F., and Seppäläinen, T · 2016
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Brownian occupation measures, compactness and large deviations
Mukherjee, C., and Varadhan, S. R. S · 2016
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Random-walk in Beta-distributed random environment
Barraquand, G., and Corwin, I · 2017
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Mean-field interaction of Brownian occupation measures II: A rigorous construction of the Pekar process
Bolthausen, E., König, W., and Mukherjee, C · 2017
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Mean-field interaction of Brownian occupation measures, I: Uniform tube property of the Coulomb functional
König, W., and Mukherjee, C · 2017
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Gibbs measures on mutually interacting Brownian paths under singularities
Mukherjee, C · 2017
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Variational formulas and disorder regimes of random walks in random potentials
Rassoul-Agha, F., Seppäläinen, T., and Yilmaz, A · 2017
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Localization of the Gaussian multiplicative chaos in the Wiener space and the stochastic heat equation in strong disorder
Bröker, Y., and Mukherjee, C · 2019
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Localization of directed polymers in continuous space
Bakhtin, Y., and Seo, D · 2020
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