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We introduce and study a new model consisting of a single classical random walker undergoing continuous monitoring at rate $\gamma$ on a discrete lattice. Although such a continuous measurement cannot affect physical observables, it has a…

Statistical Mechanics · Physics 2023-01-04 Tony Jin , David G. Martin

Scale-invariant fluctuations of growing interfaces are studied for circular clusters of an off-lattice variant of the Eden model, which belongs to the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class. Statistical properties of…

Statistical Mechanics · Physics 2012-05-15 Kazumasa A. Takeuchi

It has been discovered that the Kadomtsev-Petviashvili(KP) equation governs the distribution of the fluctuation of many random growth models, in particular, the Tracy-Widom distributions appear as special self-similar solutions of the KP…

Probability · Mathematics 2020-11-02 Xincheng Zhang

We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all…

Statistical Mechanics · Physics 2014-12-23 I. S. S. Carrasco , K. A. Takeuchi , S. C. Ferreira , T. J. Oliveira

We consider two models for directed polymers in space-time independent random media (the O'Connell-Yor semi-discrete directed polymer and the continuum directed random polymer) at positive temperature and prove their KPZ universality via…

Probability · Mathematics 2013-03-06 Alexei Borodin , Ivan Corwin , Patrik Ferrari

We study the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) interfaces growing inward from ring-shaped initial conditions, experimentally and numerically, using growth of a turbulent state in liquid-crystal electroconvection and an…

Statistical Mechanics · Physics 2017-08-14 Yohsuke T. Fukai , Kazumasa A. Takeuchi

We study height fluctuations of interfaces in the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) class, growing at different speeds in the left half and the right half of space. Carrying out simulations of the discrete polynuclear growth…

Statistical Mechanics · Physics 2018-04-18 Yasufumi Ito , Kazumasa A. Takeuchi

For stationary interface growth, governed by the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimensions, typical fluctuations of the interface height at long times are described by the Baik-Rains distribution. Recently Chhita et al. [1]…

Statistical Mechanics · Physics 2017-11-22 Baruch Meerson , Johannes Schmidt

We consider the isochrone curves in first-passage percolation on a 2D square lattice, i.e. the boundary of the set of points which can be reached in less than a given time from a certain origin. The occurrence of an instantaneous average…

We consider a model of a quenched disordered geometry in which a random metric is defined on ${\mathbb R}^2$, which is flat on average and presents short-range correlations. We focus on the statistical properties of balls and geodesics,…

Statistical Mechanics · Physics 2015-06-09 Silvia N. Santalla , Javier Rodriguez-Laguna , Tom LaGatta , Rodolfo Cuerno

The current/height fluctuation statistics of Kardar-Parisi-Zhang (KPZ) universality in 1+1 dimensions are sensitive to the initial state. We find that the averages over the initial states exhibit universal and scale-invariant patterns when…

Statistical Mechanics · Physics 2024-07-03 Johannes Schmidt , Andreas Schadschneider

The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling…

Disordered Systems and Neural Networks · Physics 2018-05-24 Alexander K. Hartmann , Pierre Le Doussal , Satya N. Majumdar , Alberto Rosso , Gregory Schehr

We study fluctuations of interfaces in the Kardar-Parisi-Zhang (KPZ) universality class with curved initial conditions. By simulations of a cluster growth model and experiments of liquid-crystal turbulence, we determine the universal…

Statistical Mechanics · Physics 2020-02-13 Yohsuke T. Fukai , Kazumasa A. Takeuchi

Circular KPZ interfaces spreading radially in the plane have GUE Tracy-Widom (TW) height distribution (HD) and Airy$_2$ spatial covariance, but what are their statistics if they evolve on the surface of a different background space, such as…

Statistical Mechanics · Physics 2019-04-03 I. S. S. Carrasco , T. J. Oliveira

Exciton-polariton condensates under driven-dissipative conditions are predicted to belong to the Kardar-Parisi-Zhang (KPZ) universality class, the dynamics of the condensate phase satisfying the same equation as for classical stochastic…

Statistical Mechanics · Physics 2024-08-29 Konstantinos Deligiannis , Davide Squizzato , Anna Minguzzi , Léonie Canet

A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…

Chaotic Dynamics · Physics 2012-03-28 Giorgio Krstulovic , Rehab Bitane , Jeremie Bec

We investigate the radius distributions (RD) of surfaces obtained with large-scale simulations of radial clusters that belong to the KPZ universality class. For all investigated models, the RDs are given by the Tracy-Widom distribution of…

Statistical Mechanics · Physics 2011-11-10 S. G. Alves , T. J. Oliveira , S. C. Ferreira

In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This…

Mathematical Physics · Physics 2011-03-01 Patrik L. Ferrari

The probability distribution for the free energy of directed polymers in random media (DPRM) with uncorrelated noise in $d=1+1$ dimensions satisfies the Tracy-Widom distribution. We inquire if and how this universal distribution is modified…

Statistical Mechanics · Physics 2016-07-06 Sherry Chu , Mehran Kardar

The statistics of the fluctuations of quantum many-body systems are highly revealing of their nature. In driven-dissipative systems displaying macroscopic quantum coherence, as exciton polariton condensates under incoherent pumping, the…