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Related papers: Noise sensitivity in last-passage percolation

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We consider the system of one-sided reflected Brownian motions which is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and…

Probability · Mathematics 2021-08-30 Mihai Nica , Jeremy Quastel , Daniel Remenik

Consider the model where nodes are initially distributed as a Poisson point process with intensity $\lambda$ over $\mathbb{R}^d$ and are moving in continuous time according to independent Brownian motions. We assume that nodes are capable…

Probability · Mathematics 2015-09-10 Alexandre Stauffer

We study the two-time distribution in directed last passage percolation with geometric weights in the first quadrant. We compute the scaling limit and show that it is given by a contour integral of a Fredholm determinant.

Probability · Mathematics 2018-11-07 Kurt Johansson

Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its…

Probability · Mathematics 2011-11-03 Ivan Corwin

In this paper, we consider nearest-neighbor oriented percolation with independent Bernoulli bond-occupation probability on the $d$-dimensional body-centered cubic (BCC) lattice $\mathbb{L}^d$ and the set of non-negative integers…

Mathematical Physics · Physics 2022-07-19 Lung-Chi Chen , Satoshi Handa , Yoshinori Kamijima

The prediction of diffusion in solids is necessary to understand the microstructure evolution in materials out of equilibrium. Although one can reasonably predict diffusive transport coefficients using atomistic methods, these approaches…

Materials Science · Physics 2025-08-07 Jacob Jeffries , Emilio Mendoza Reyes , Fadi Abdeljawad , Murray Daw , Enrique Martinez

We consider a variant of the continuous and discrete Ulam-Hammersley problems: we study the maximal length of an increasing path through a Poisson point process (or a Bernoulli point process) with the restriction that there must be minimal…

Probability · Mathematics 2019-03-13 Anne-Laure Basdevant , Lucas Gerin

We show that on a Cayley graph of a nonamenable group, almost surely the infinite clusters of Bernoulli percolation are transient for simple random walk, that simple random walk on these clusters has positive speed, and that these clusters…

Probability · Mathematics 2007-05-23 Itai Benjamini , Russell Lyons , Oded Schramm

We present a numerical study of noise correlations, i.e., density-density correlations in momentum space, in the extended fermionic Hubbard model in one dimension. In experiments with ultracold atoms, these noise correlations can be…

Strongly Correlated Electrons · Physics 2007-10-29 Andreas Luscher , Andreas Laeuchli , Reinhard M. Noack

Recent experiments have shown that the spontaneous activity of young dissociated neuronal cultures can be described as a process of highly inhomogeneous nucleation and front propagation due to the localization of noise activity, i.e., noise…

Neurons and Cognition · Quantitative Biology 2021-05-26 Javier G. Orlandi , Jaume Casademunt

We show non-existence of non-trivial bi-infinite geodesics in the solvable last-passage percolation model with i.i.d. geometric weights. This gives the first example of a model with discrete weights where non-existence of non-trivial…

Probability · Mathematics 2021-12-02 Sean Groathouse , Christopher Janjigian , Firas Rassoul-Agha

In last passage percolation models lying in the KPZ universality class, the energy of long energy-maximizing paths may be studied as a function of the paths' pair of endpoint locations. Scaled coordinates may be introduced, so that these…

Probability · Mathematics 2019-04-17 Alan Hammond

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…

Probability · Mathematics 2021-08-26 Erik Bates , Shirshendu Ganguly , Alan Hammond

We study the directed last-passage percolation model on the planar integer lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside the class of exactly solvable models. In a previous paper we constructed…

Probability · Mathematics 2016-07-26 Nicos Georgiou , Firas Rassoul-Agha , Timo Seppäläinen

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…

We measure the noise correlations of two-dimensional (2D) Bose gases after free expansion, and use them to characterize the in-situ phase coherence across the Berezinskii-Kosterlitz-Thouless (BKT) transition. The noise-correlation function…

In discrete models describing growing rough interfaces of the Kardar-Parisi-Zhang universality class, we examine height fluctuations at a fixed site as a function of time in the monolayer unit. For small systems, we show that it is possible…

Statistical Mechanics · Physics 2026-03-20 Rahul Chhimpa , Avinash Chand Yadav

One-dependent first passage percolation is a spreading process on a graph where the transmission time through each edge depends on the direct surroundings of the edge. In particular, the classical iid transmission time $L_{xy}$ is…

Probability · Mathematics 2024-03-26 Júlia Komjáthy , John Lapinskas , Johannes Lengler , Ulysse Schaller

Weak lensing experiments are a powerful probe of cosmology through their measurement of the mass distribution of the universe. A challenge for this technique is to control systematic errors that occur when measuring the shapes of distant…

Cosmology and Nongalactic Astrophysics · Physics 2015-06-04 Alexandre Refregier , Tomasz Kacprzak , Adam Amara , Sarah Bridle , Barnaby Rowe

We prove that the supercritical phase of Voronoi percolation on $\mathbb{R}^d$, $d\geq 3$, is well behaved in the sense that for every $p>p_c(d)$ local uniqueness of macroscopic clusters happens with high probability. As a consequence,…

Probability · Mathematics 2024-10-25 Barbara Dembin , Franco Severo