@article{556,
abstract = {We investigate the free boundary Schur process, a variant of the Schur process introduced by Okounkov and Reshetikhin, where we allow the first and the last partitions to be arbitrary (instead of empty in the original setting). The pfaffian Schur process, previously studied by several authors, is recovered when just one of the boundary partitions is left free. We compute the correlation functions of the process in all generality via the free fermion formalism, which we extend with the thorough treatment of “free boundary states.” For the case of one free boundary, our approach yields a new proof that the process is pfaffian. For the case of two free boundaries, we find that the process is not pfaffian, but a closely related process is. We also study three different applications of the Schur process with one free boundary: fluctuations of symmetrized last passage percolation models, limit shapes and processes for symmetric plane partitions and for plane overpartitions.},
author = {Betea, Dan and Bouttier, Jeremie and Nejjar, Peter and Vuletic, Mirjana},
issn = {14240637},
journal = {Annales Henri Poincare},
number = {12},
pages = {3663--3742},
publisher = {Fakultät für Mathematik Universität Wien},
title = {{The free boundary Schur process and applications}},
doi = {10.1007/s00023-018-0723-1},
volume = {19},
year = {2018},
}
@article{70,
abstract = {We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by a≥0, which creates a shock in the particle density of order aT−1/3, T the observation time. When starting from step initial data, we provide bounds on the limiting law which in particular imply that in the double limit lima→∞limT→∞ one recovers the product limit law and the degeneration of the correlation length observed at shocks of order 1. This result is shown to apply to a general last-passage percolation model. We also obtain bounds on the two-point functions of several airy processes.},
author = {Nejjar, Peter},
issn = {1980-0436},
journal = {Latin American Journal of Probability and Mathematical Statistics},
number = {2},
pages = {1311--1334},
publisher = {ALEA},
title = {{Transition to shocks in TASEP and decoupling of last passage times}},
doi = {10.30757/ALEA.v15-49},
volume = {15},
year = {2018},
}
@unpublished{72,
abstract = {We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle initially at the origin. For ρ<λ, there is a shock and the second class particle moves with speed 1−λ−ρ. For large time t, we show that the position of the second class particle fluctuates on a t1/3 scale and determine its limiting law. We also obtain the limiting distribution of the number of steps made by the second class particle until time t.},
author = {Ferrari, Patrick and Nejjar, Peter and Ghosal, Promit},
booktitle = {ArXiv},
publisher = {ArXiv},
title = {{Limit law of a second class particle in TASEP with non-random initial condition}},
year = {2018},
}
@article{447,
abstract = {We consider last passage percolation (LPP) models with exponentially distributed random variables, which are linked to the totally asymmetric simple exclusion process (TASEP). The competition interface for LPP was introduced and studied in Ferrari and Pimentel (2005a) for cases where the corresponding exclusion process had a rarefaction fan. Here we consider situations with a shock and determine the law of the fluctuations of the competition interface around its deter- ministic law of large number position. We also study the multipoint distribution of the LPP around the shock, extending our one-point result of Ferrari and Nejjar (2015).},
author = {Ferrari, Patrik and Nejjar, Peter},
journal = {Revista Latino-Americana de Probabilidade e Estatística},
pages = {299 -- 325},
publisher = {ALEA Network},
title = {{Fluctuations of the competition interface in presence of shocks}},
volume = {9},
year = {2017},
}