Tootfinder

Metastable transition times of the 1D dynamical sine-Gordon model
Petri Laarne
https://arxiv.org/abs/2509.13806 https://arxiv.org/pdf/2509.13806

Metastable transition times of the 1D dynamical sine-Gordon model
We study the dynamics of a stochastic heat equation with $γ\sin(βu)$ nonlinearity on one-dimensional torus. We show an Eyring--Kramers law for the jump rate between potential wells in the small-noise limit, and that the transition state undergoes a bifurcation at $γβ= 1$. The argument follows the potential-theoretic approach of Berglund and Gentz [Electron. J. Probab. 2013].

@… just drag your feet walking in a squircle. Then jump in the middle and walk back and forth bin the shape of a V, then get your child to take a picture. 😁 @…

MHD Rankine-Hugoniot jump conditions for shock waves in van der Waals gases
Raj Kumar Anand
https://arxiv.org/abs/2507.07564 https://…

MHD Rankine-Hugoniot jump conditions for shock waves in van der Waals gases
In this article, we have presented non-relativistic boundary conditions across a magnetohydrodynamic (MHD) shock front propagating in van der Waals gases. The expression for the strength of the non-relativistic MHD shock wave has been obtained, and the Rankine-Hugoniot (R-H) shock jump relations, or boundary conditions, for the pressure, the density, and the particle velocity across an MHD shock front have been derived in terms of a shock compression ratio. The simplified forms of shock jump re…

Master equations for continuous-time random walks with stochastic resetting
Fausto Colantoni, Gianni Pagnini
https://arxiv.org/abs/2507.07590 https://

Master equations for continuous-time random walks with stochastic resetting
We study a general continuous-time random walk (CTRW), by including non-Markovian cases and Lévy flights, under complete stochastic resetting to the initial position with an arbitrary law, which can be power-lawed as well as Poissonian. We provide three linked results. First, we show that the random walk under stochastic resetting is a CTRW with the same jump-size distribution of the non-reset original CTRW but different counting process. Later, we derive the condition for a CTRW with stochast…

Multicentered black hole saddles for supersymmetric indices
Jan Boruch, Luca V. Iliesiu, Sameer Murthy, Gustavo J. Turiaci
https://arxiv.org/abs/2507.07166

Multicentered black hole saddles for supersymmetric indices
The supersymmetric index in string theory can sometimes have a discontinuous integer-valued jump at co-dimension one surfaces in moduli space called walls of marginal stability. When the index counts black hole microstates, crossing such walls of marginal stability amounts to the appearance or disappearance of a large number of such states. While wall-crossing has been understood in string theory and through the disappearance of extremal Lorentzian supergravity solutions as the moduli are varie…

Examples of stable-like random walks on groups of polynomial growth
Laurent Saloff-Coste, Ruoqi Zhang
https://arxiv.org/abs/2509.00970 https://arxiv.org/pd…

Examples of stable-like random walks on groups of polynomial growth
We consider several families of long jump random walks on groups of polynomial volume growth which are naturally expected to have a stable-like behavior. We then prove optimal pseudo-Poincaré inequalities for these walks. These pseudo-Poincaré inequalities allow us to show that the random walks in questions indeed have a stable-like behavior and to obtain detailed estimates.

Walk-on-Interfaces: A Monte Carlo Estimator for an Elliptic Interface Problem with Nonhomogeneous Flux Jump Conditions and a Neumann Boundary Condition
Xinwen Ding, Adam R Stinchcombe
https://arxiv.org/abs/2508.16767

Walk-on-Interfaces: A Monte Carlo Estimator for an Elliptic Interface Problem with Nonhomogeneous Flux Jump Conditions and a Neumann Boundary Condition
Elliptic interface problems arise in numerous scientific and engineering applications, modeling heterogeneous materials in which physical properties change discontinuously across interfaces. In this paper, we present \textit{Walk-on-Interfaces} (WoI), a grid-free Monte Carlo estimator for a class of Neumann elliptic interface problems with nonhomogeneous flux jump conditions. Our Monte Carlo estimators maintain consistent accuracy throughout the domain and, thus, do not suffer from the well-kno…

A Universal Vehicle-Trailer Navigation System with Neural Kinematics and Online Residual Learning
Yanbo Chen, Yunzhe Tan, Yaojia Wang, Zhengzhe Xu, Junbo Tan, Xueqian Wang
https://arxiv.org/abs/2507.15607

A Universal Vehicle-Trailer Navigation System with Neural Kinematics and Online Residual Learning
Autonomous navigation of vehicle-trailer systems is crucial in environments like airports, supermarkets, and concert venues, where various types of trailers are needed to navigate with different payloads and conditions. However, accurately modeling such systems remains challenging, especially for trailers with castor wheels. In this work, we propose a novel universal vehicle-trailer navigation system that integrates a hybrid nominal kinematic model--combining classical nonholonomic constraints …

Sprinkled Decoupling for Hammersley's Process
Leandro P. R. Pimentel, Roberto Viveros
https://arxiv.org/abs/2506.19008 https://ar…

Sprinkled Decoupling for Hammersley's Process
In this article we prove a sprinkled decoupling inequality for the stationary Hammersley's interacting particle process. Inspired by the work of Baldasso and Texeira (2018), and Hilário, Kious and Texeira (2020), we apply this inequality to study two distinct problems on the top of this particle process. First, we analyze a detection problem, demonstrating that a fugitive can evade particles, provided that their jump range is sufficiently large. Second, we show that a random walk in a dynamic …