Related papers: Macroscopic behavior of Lipschitz random surfaces
The current paper is devoted to the study of existence, uniqueness and Lifshitz tails of the integrated density of surface states (IDSS) for Schr\"{o}dinger operators with alloy type random surface potentials. We prove the existence and…
In this work, we study the Anderson model on the Sierpinski gasket graph. We first identify the almost sure spectrum of the Anderson model when the support of the random potential has no gaps. We then prove the existence of the integrated…
We study the consistency of Lipschitz learning on graphs in the limit of infinite unlabeled data and finite labeled data. Previous work has conjectured that Lipschitz learning is well-posed in this limit, but is insensitive to the…
Motivated by questions on the delocalization of random surfaces, we prove that random surfaces satisfying a Lipschitz constraint rarely develop extremal gradients. Previous proofs of this fact relied on reflection positivity and were thus…
Under general assumptions on the target distribution $p^\star$, we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with optimal dependence on time and dimension. As applications, we…
Lipschitz continuity is a crucial functional property of any predictive model, that naturally governs its robustness, generalisation, as well as adversarial vulnerability. Contrary to other works that focus on obtaining tighter bounds and…
Realistic fluid-solid interaction potentials are essential in description of confined fluids especially in the case of geometric heterogeneous surfaces. Correlated random field is considered as a model of random surface with high geometric…
The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep…
We investigate the integrated density of states of the Schr\"odinger operator in the Euclidean plane with a perpendicular constant magnetic field and a random potential. For a Poisson random potential with a non-negative algebraically…
This paper demonstrates the robustness of Lipschitz-regularized $\alpha$-divergences as objective functionals in generative modeling, showing they enable stable learning across a wide range of target distributions with minimal assumptions.…
Electronic properties of amorphous or non-crystalline disordered solids are often modelled by one-particle Schroedinger operators with random potentials which are ergodic with respect to the full group of Euclidean translations. We give a…
This paper is devoted to investigating the random dynamics of stochastic discrete long-wave-short-wave resonance equations, which are characterized by the following features: $(1)$ the equations contain locally Lipschitz nonlinear coupling…
Tackling semi-supervised learning problems with graph-based methods has become a trend in recent years since graphs can represent all kinds of data and provide a suitable framework for studying continuum limits, e.g., of differential…
This paper studies the long-time behavior of stochastic differential inclusions driven by maximal monotone operators, motivated by continuous-time models of first-order optimization methods under noisy or approximate operator information.…
The surface impedance approach to the description of the thermal Casimir effect in the case of real metals is elaborated starting from the free energy of oscillators. The Lifshitz formula expressed in terms of the dielectric permittivity…
We consider deep neural networks with a Lipschitz continuous activation function and with weight matrices of variable widths. We establish a uniform convergence analysis framework in which sufficient conditions on weight matrices and bias…
Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space, and properties of generated $\sigma$-ideals are studied. These $\sigma$-ideals naturally appear in the differentiation theory and in the abstract…
For a bounded Lipschitz domain with Lipschitz interface we show the following compactness theorem: Any $L^2$-bounded sequence of vector fields with $L^2$-bounded rotations and $L^2$-bounded divergences as well as $L^2$-bounded tangential…
Ferromagnetic materials exhibit anisotropy, saturation, and hysteresis. We here study the incorporation of an incremental vector hysteresis model representing such complex behavior into nonlinear magnetic field problems both, from a…
In this paper we study Lifshitz tails for continuous Laplacian in a continuous site percolation situation. By this we mean that we delete a random set $\Gamma_\omega$ from $IR^d$ and consider the Dirichlet or Neumann Laplacian on…