Related papers: Large Deviation Principle for Last Passage Percola…

In this note, we prove convergence of the half-space exponential last passage percolation (LPP) model, away from the boundary, to the directed landscape. Our approach couples the half-space and full-space LPP models and constructs two…

Last passage percolation (LPP) is a model of a directed metric and a zero-temperature polymer where the main observable is a directed path evolving in a random environment accruing as energy the sum of the random weights along itself. When…

We prove that two half-space models in the KPZ universality class, exponential last-passage percolation and a family of Poisson-avoiding metrics generalizing colored TASEP, converge to a common scaling limit. This scaling limit is the…

This short note provides a large-deviation-based upper bound on the growth rate of directed last passage percolation (LPP) using the entropy of the normalized direction vector.

Directed last passage percolation models on the plane, where one studies the weight as well as the geometry of optimizing paths (called polymers) in a field of i.i.d. weights, are paradigm examples of models in the KPZ universality class.…

The study of transversal fluctuations of the optimal path is a crucial aspect of the Kardar-Parisi-Zhang (KPZ) universality class. In this work, we establish the large deviation limit for the midpoint transversal fluctuations in a general…

This paper studies the large scale limits of multi-type invariant distributions and Busemann functions of planar stochastic growth models in the Kardar-Parisi-Zhang (KPZ) class. We identify a set of sufficient hypotheses for convergence of…

It is believed that for metric-like models in the KPZ class the following property holds: with probability one, starting from any point, there are at most two semi-infinite geodesics with the same direction that do not coalesce. Until now,…

We prove the upper-tail Large Deviation Principle (LDP) for the parabolic Airy process and characterize the limit shape of the directed landscape under the upper-tail conditioning. The LDP result answers Conjecture 10.1 in Das, Dauvergne,…

The conjectured limit of last passage percolation is a scale-invariant, independent, stationary increment process with respect to metric composition. We prove this for Brownian last passage percolation. We construct the Airy sheet and…

This note establishes a universal directed landscape limit for last passage percolation models in an intermediate scaling regime. We find as a quick consequence the transversal fluctuations for geodesics taken near the axis. We extend the…

We consider a sequence of processes defined on half-line for all non negative t. We give sufficient conditions for Large Deviation Principle (LDP) to hold in the space of continuous functions with a new metric that is more sensitive to…

We provide a framework for proving convergence to the directed landscape, the central object in the Kardar-Parisi-Zhang universality class. For last passage models, we show that compact convergence to the Airy line ensemble implies…

We study maximal length collections of disjoint paths, or 'disjoint optimizers', in the directed landscape. We show that disjoint optimizers always exist, and that their lengths can be used to construct an extended directed landscape. The…

We study the last passage time in geometric last passage percolation (LPP). As the system size increases, we derive precise large deviation probabilities -- up to and including the constant terms -- for both the lower and upper tails. A key…

Geodesic coalescence, or the tendency of geodesics to merge together, is a hallmark phenomenon observed in a variety of planar random geometries involving a random distortion of the Euclidean metric. As a result of this, the union of…

The directed last passage percolation (LPP) on the quarter-plane is a growing model. To come into the growing set, a cell needs that the cells on its bottom and on its left to be in the growing set, and then to wait a random time. We…

In the present article we consider a natural generalization of Hammersley's Last Passage Percolation (LPP) called Entropy-controlled Last Passage Percolation (E-LPP), where points can be collected by paths with a global (entropy) constraint…

Within the Kardar-Parisi-Zhang universality class, the space-time Airy sheet is conjectured to be the canonical scaling limit for last passage percolation models. In recent work arXiv:1812.00309 of Dauvergne, Ortmann, and Vir\'ag, this…

The directed landscape is a random directed metric on the plane that arises as the scaling limit of classical metric models in the KPZ universality class. Typical pairs of points in the directed landscape are connected by a unique geodesic.…