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A differential version of the classical Weil descent is established in all characteristics. It yields a theory of differential restriction of scalars for differential varieties over finite differential field extensions. This theory is then…
We consider gradient fields $(\phi_x:x\in \mathbb{Z}^d)$ whose law takes the Gibbs--Boltzmann form $Z^{-1}\exp\{-\sum_{< x,y>}V(\phi_y-\phi_x)\}$, where the sum runs over nearest neighbors. We assume that the potential $V$ admits the…
Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…
We study diffusion in systems of classical particles whose dynamics conserves the total center of mass. This conservation law leads to several interesting consequences. In finite systems, it allows for equilibrium distributions that are…
We have obtained some upper bounds for the probability distribution of extremes of a self-similar Gaussian random field with stationary rectangular increments that are defined on the compact spaces. The probability distributions of extremes…
We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and…
A new method for approximating fractional derivatives of the Gaussian function and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann-Liouville integral using polynomial…
Totally symmetric arbitrary spin conformal fields in (A)dS space of even dimension greater than or equal to four are studied. Ordinary-derivative and gauge invariant Lagrangian formulation for such fields is obtained. Gauge symmetries are…
We study gauge fixing via the standard local extremization algorithm for 2-dimensional $U(1)$. On a lattice with spherical topology $S^2$ where all copies are lattice artifacts, we find that the number of these 'Gribov' copies diverges in…
We discuss the derivation and the solutions of integro-differential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time…
Recent lattice calculations have confirmed that QCD static potential for sources in different representations of the gauge group is proportional to eigenvalue of the corresponding quadratic Casimir operator with an accuracy of a few…
We obtain a complete description of local anisotropic scaling limits for a class of fractional random fields $X$ on ${\mathbb{R}}^2$ written as stochastic integral with respect to infinitely divisible random measure. The scaling procedure…
We study the large-scale behavior of the height function in the dimer model on the square lattice. Richard Kenyon has shown that the fluctuations of the height function on Temperleyan discretizations of a planar domain converge in the…
We study the scaling limit of a divisible sandpile model associated to a truncated $\alpha$-stable random walk. We prove that the limiting distribution is related to an obstacle problem for a truncated fractional Laplacian. We also provide,…
The paper presents bounds for the distributions of suprema for a particular class of sub-Gaussian type random fields defined over spaces with anisotropic metrics. The results are applied to random fields related to stochastic heat equations…
The paper study the discrete sets of translations of the Gaussian function that span the spaces L1(R) and L2(R).
We study a fractional differentiation operator for functions on the conjugate space to an infinite extension of a local field of zero characteristic which is a union of an increasing sequence of finite extensions. In particular, a…
Motivated by Applied Physics and Photonics studies of random resonators, we study in the stochastic part of this paper random acoustic operators in non-smooth bounded domains $G \subset \mathbb{R}^d$ and introduce m-dissipative impedance…
This article investigates nonlocal, fully nonlinear generalizations of the classical biharmonic operator $(-\Delta)^2$. These fractional $p$-biharmonic operators appear naturally in the variational characterization of the optimal fractional…
This paper investigates the scaling limit of one--dimensional lattice Ising--Kac--Kawasaki dynamics. Starting from a martingale formulation for the Kac coarse-grained field $X_\gamma$, we decompose the dynamics into a discrete conservative…