[BOOK][B] Directed polymers in random environments
F Comets - 2017 - Springer
This monograph contains the notes of lectures I gave in Saint Flour Probability Summer
School in July 2016. The two other courses were given by Paul Bourgade and by Scott …
School in July 2016. The two other courses were given by Paul Bourgade and by Scott …
Variational formulas and cocycle solutions for directed polymer and percolation models
We discuss variational formulas for the law of large numbers limits of certain models of
motion in a random medium: namely, the limiting time constant for last-passage percolation …
motion in a random medium: namely, the limiting time constant for last-passage percolation …
Fluctuations of partition functions of directed polymers in weak disorder beyond the -phase
S Junk - arxiv preprint arxiv:2202.02907, 2022 - arxiv.org
We study the directed polymer model in a bounded environment in weak disorder but
without $ L^ 2$-boundedness, specifically the speed of homogenization for the field …
without $ L^ 2$-boundedness, specifically the speed of homogenization for the field …
Large deviation rate functions for the partition function in a log-gamma distributed random potential
N Georgiou, T Seppäläinen - 2013 - projecteuclid.org
We study right tail large deviations of the logarithm of the partition function for directed lattice
paths in iid random potentials. The main purpose is the derivation of explicit formulas for the …
paths in iid random potentials. The main purpose is the derivation of explicit formulas for the …
Aging for the stationary Kardar-Parisi-Zhang equation and related models
We study the aging property for stationary models in the KPZ universality class. In particular,
we show aging for the stationary KPZ fixed point, the Cole-Hopf solution to the stationary …
we show aging for the stationary KPZ fixed point, the Cole-Hopf solution to the stationary …
Concentrations for the simple random walk in unbounded nonnegative potentials
N Kubota - arxiv preprint arxiv:1504.06822, 2015 - arxiv.org
We consider the simple random walk in iid nonnegative potentials on the multidimensional
cubic lattice. Our goal is to investigate the cost paid by the simple random walk for traveling …
cubic lattice. Our goal is to investigate the cost paid by the simple random walk for traveling …
Semimartingale Approach and Localization Transition
F Comets, F Comets - Directed Polymers in Random Environments: École …, 2017 - Springer
The next step in our martingale analysis is to consider ln W n as a semimartingale and to
write its Doob's decomposition. Viewed as a “conditional second moment” method, this new …
write its Doob's decomposition. Viewed as a “conditional second moment” method, this new …
The Martingale Approach and the L 2 Region
F Comets, F Comets - Directed Polymers in Random Environments: École …, 2017 - Springer
Martingale theory is well-known as a powerful tool to study random sequences. In this
section, we start to use it in our context. First of all, it is efficient for proving that equality can …
section, we start to use it in our context. First of all, it is efficient for proving that equality can …
[PDF][PDF] Large deviation rate functions for the partition function in a log-gamma distributed random particle
N Georgiou, T Seppäläinen - 2012 - sussex.figshare.com
We study right tail large deviations of the logarithm of the partition function for directed lattice
paths in iid random potentials. The main purpose is the derivation of explicit formulas for the …
paths in iid random potentials. The main purpose is the derivation of explicit formulas for the …
Modèles de polymères dirigés en milieux aléatoires
GM Flores - 2010 - theses.hal.science
Nous étudions plusieurs modèles de polymères dirigés en milieux aléatoires. Pour le
modèle classique sur Z^ d, nous étudions la convergence de l'environnement vu par la …
modèle classique sur Z^ d, nous étudions la convergence de l'environnement vu par la …