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Sepp\"al\"ainen and Valk\'o showed in \cite{SV} that for a suitable choice of parameters, the variance growth of the free energy of the stationary O'Connell-Yor polymer is governed by the exponent $2/3$, characteristic of models in the KPZ…

Probability · Mathematics 2020-04-14 Christian Noack , Philippe Sosoe

We elucidate the universal spatio-temporal scaling properties of the time-dependent correlation functions in a class of two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion process. By…

Statistical Mechanics · Physics 2024-06-17 Pritha Dolai , Aditi Simha , Abhik Basu

We obtain several exact results for universal distributions involving the maximum of the Airy$_2$ process minus a parabola and plus a Brownian motion, with applications to the 1D Kardar-Parisi-Zhang (KPZ) stochastic growth universality…

Disordered Systems and Neural Networks · Physics 2017-12-13 Pierre Le Doussal

We analyze the freezing and collapse transition of a simple model for flexible polymer chains on simple cubic and face-centered cubic lattices by means of sophisticated chain-growth methods. In contrast to bond-fluctuation polymer models in…

Soft Condensed Matter · Physics 2009-02-16 Thomas Vogel , Michael Bachmann , Wolfhard Janke

We present a systematic short time expansion for the generating function of the one point height probability distribution for the KPZ equation with droplet initial condition, which goes much beyond previous studies. The expansion is checked…

Statistical Mechanics · Physics 2018-11-21 Alexandre Krajenbrink , Pierre Le Doussal , Sylvain Prolhac

Motivated by the recent exact solution of the {\it stationary-state} Kardar-Parisi-Zhang (KPZ) statistics by Imamura & Sasamoto (Phys. Rev. Lett. {\bf 108}, 190603 (2012)), as well as a precursor experimental signature unearthed by Takeuchi…

Statistical Mechanics · Physics 2014-03-31 Timothy Halpin-Healy , Yuexia Lin

We consider an inverse problem governed by the initial-boundary value problem for the thermoviscoelastic Kelvin-Voigt system \begin{align*}\left\{ \begin{array}{l} \rho(z,t) u_{tt}- \left(\Gamma(\Theta) u_{zt} +p(z,t) u_z…

Analysis of PDEs · Mathematics 2026-02-18 Torben J. Fricke , Raphael Kuess , Felix Meyer

Heat flows in 1+1 dimensional stochastic environment converge after scaling to the random geometry described by the directed landscape. In this first part, we show that the O'Connell-Yor polymer and the KPZ equation converge to the KPZ…

Probability · Mathematics 2020-08-18 Balint Virag

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 identify the integrable stopping time $\tau_*$ with minimal $L^1$-distance to the last-passage time $\gamma_z$ to a given level $z>0$, for an arbitrary non-negative time-homogeneous transient diffusion $X$. We demonstrate that $\tau_*$…

Probability · Mathematics 2013-12-31 Kristoffer Glover , Hardy Hulley

We present an exact solution for the height distribution of the KPZ equation at any time $t$ in a half space with flat initial condition. This is equivalent to obtaining the free energy distribution of a polymer of length $t$ pinned at a…

Statistical Mechanics · Physics 2023-02-24 Guillaume Barraquand , Pierre Le Doussal

We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…

Probability · Mathematics 2023-07-05 Theodoros Assiotis

The study of first passage percolation (FPP) for the random interlacements model has been initiated in arXiv:2112.12096, where it is shown that on $\mathbb{Z}^d$, $d\geq 3$, the FPP distance is comparable to the graph distance with high…

Probability · Mathematics 2025-10-15 Alexis Prévost

We consider the initial boundary value problem for the time-fractional diffusion equation with a homogeneous Dirichlet boundary condition and an inhomogeneous initial data $a(x)\in L^{2}(D)$ in a bounded domain $D\subset \mathbb{R}^d$ with…

Numerical Analysis · Mathematics 2020-02-19 Jiuhua Hu , Guanglian Li

We study dynamical spin correlations in a dissipative XXZ spin chain subject to uniform local spin-loss and pumping. Starting from a mixed steady state that is featureless albeit possessing finite magnetization, rich dynamics emerges in…

Strongly Correlated Electrons · Physics 2026-05-07 Cătălin Paşcu Moca , Doru Sticlet , Ovidiu I. Pâţu , Balazs Dóra

Describing the dynamics and thermodynamics of amorphous materials near the glass transition is a major challenge in soft-matter physics and polymer engineering. Here, we show that the dependence of the dielectric alpha-relaxation time on…

Soft Condensed Matter · Physics 2025-04-28 Valeriy V. Ginzburg , Oleg V. Gendelman , Riccardo Casalini , Alessio Zaccone

For models in the KPZ universality class, such as the zero temperature model of planar last passage-percolation (LPP) and the positive temperature model of directed polymers, its upper tail behavior has been a topic of recent interest, with…

Probability · Mathematics 2025-12-23 Shirshendu Ganguly , Milind Hegde , Lingfu Zhang

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

Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…

Probability · Mathematics 2018-04-17 Michael Damron

Obtaining the exact multi-time correlations for one-dimensional growth models described by the Kardar-Parisi-Zhang (KPZ) universality class is presently an outstanding open problem. Here, we study the joint probability distribution function…

Statistical Mechanics · Physics 2017-07-05 Jacopo de Nardis , Pierre Le Doussal