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We describe a directed avalanche model; a slowly unloading sandbox driven by lowering a retaining wall. The directness of the dynamics allows us to interpret the stable sand surfaces as world sheets of fluctuating interfaces in one lower…

Statistical Mechanics · Physics 2009-11-07 Chun-Chung Chen , Marcel den Nijs

We consider the KPZ equation in one space dimension driven by a stationary centred space-time random field, which is sufficiently integrable and mixing, but not necessarily Gaussian. We show that, in the weakly asymmetric regime, the…

Probability · Mathematics 2016-10-21 Martin Hairer , Hao Shen

Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be…

Statistical Mechanics · Physics 2015-10-07 Guy Bunin , Yariv Kafri , Daniel Podolsky

One of the main difficulties in proving convergence of discrete models of surface growth to the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than one is that the correct way to take a scaling limit, so that the limit is…

Probability · Mathematics 2022-11-30 Sourav Chatterjee

Universal behavior in far-from-equilibrium systems is driven by interactions between transport processes and noise structure. The Kardar-Parisi-Zhang (KPZ) framework predicts that extensions incorporating conserved currents or temporally…

The universality of the directed polymer model and the analogous KPZ equation is supported by numerical simulations using non-Gaussian random probability distributions in two, three and four dimensions. It is shown that although in the…

Disordered Systems and Neural Networks · Physics 2016-08-31 Ehud Perlsman , Shlomo Havlin

We show that effective interactions mediated by disorder between two directed polymers can be modelled as the crosscorrelation of noises in the Kardar-Parisi-Zhang (KPZ) equations satisfied by the respective free energies of these polymers.…

Condensed Matter · Physics 2009-10-31 Abhik Basu

A variational method that allows for replica-symmetry breaking is applied to directed polymers in an (N+1)-dimensional disordered medium. The noise studied here has gaussian correlations, i.e. it is short-ranged. In dimensions N<2, the…

Condensed Matter · Physics 2007-05-23 T. Blum

In this paper, the problem of distributed optimization is studied via a network of agents. Each agent only has access to a noisy gradient of its own objective function, and can communicate with its neighbors via a network. To handle this…

Optimization and Control · Mathematics 2025-06-19 Yuchen Yang , Kaihong Lu , Long Wang

We report on the effect of spatially correlated noise on the velocities of self propelled particles. Correlations in the random forces acting on self propelled particles can induce directed collective motion, i.e. swarming. Even with…

Soft Condensed Matter · Physics 2022-12-21 Chunming Zheng , Ralf Tönjes

We study the simple, linear, Edwards-Wilkinson equation that describes surface growth governed by height diffusion in the presence of spatiotemporally power-law decaying correlated noise. We analytically show that the surface becomes…

Pattern Formation and Solitons · Physics 2020-04-22 Alejandro Alés , Juan M López

We present an exactly solvable nonlinear model for the directed motion of an object due to zero-mean fluctuations on a uniform featureless surface. Directed motion results from the effect of dry (Coulombic) friction coupled to asymmetric…

Statistical Mechanics · Physics 2012-11-02 Adrian Baule , Peter Sollich

Results of experiments on the dynamics and kinetic roughening of one-dimensional slow-combustion fronts in three grades of paper are reported. Extensive averaging of the data allows a detailed analysis of the spatial and temporal…

Statistical Mechanics · Physics 2009-11-07 M. Myllys , J. Maunuksela , M. Alava , T. Ala-Nissila , J. Merikoski , J. Timonen

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…

Probability · Mathematics 2022-10-13 Duncan Dauvergne , Bálint Virág

In this paper we consider directed walks on a tree with a fixed branching ratio K at a finite temperature T. We consider the case where each site (or link) is assigned a random energy uncorrelated in time, but correlated in the transverse…

Condensed Matter · Physics 2009-10-31 Yadin Y. Goldschmidt

In metrological tasks, employing entanglement can quantitatively improve the precision of parameter estimation. However, susceptibility of the entanglement to decoherence fades this capability in the realistic metrology and limits ultimate…

Quantum Physics · Physics 2017-05-04 R. Yousefjani , S. Salimi , A. S. Khorashad

Autonomous (noise-agnostic) generative models, such as Equilibrium Matching and blind diffusion, challenge the standard paradigm by learning a single, time-invariant vector field that operates without explicit noise-level conditioning.…

Machine Learning · Computer Science 2026-02-23 Mojtaba Sahraee-Ardakan , Mauricio Delbracio , Peyman Milanfar

We establish fundamental properties of infinite geodesics and competition interfaces in the directed landscape. We construct infinite geodesics in the directed landscape, establish their uniqueness and coalescence, and define Busemann…

Probability · Mathematics 2025-07-08 Mustazee Rahman , Balint Virag

We study the non-convex optimization landscape for maximum likelihood estimation in the discrete orbit recovery model with Gaussian noise. This model is motivated by applications in molecular microscopy and image processing, where each…

Statistics Theory · Mathematics 2021-03-02 Zhou Fan , Yi Sun , Tianhao Wang , Yihong Wu

We show that geodesics in the directed landscape have $3/2$-variation and that weight functions along the geodesics have cubic variation. We show that the geodesic and its landscape environment around an interior point has a small-scale…

Probability · Mathematics 2024-10-31 Duncan Dauvergne , Sourav Sarkar , Bálint Virág