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We investigate Markovian lifts of stochastic Volterra equations (SVEs) with completely monotone kernels and general coefficients within a class of weighted Sobolev spaces. Our primary focus is developing a comprehensive solution theory for…

The assumption of local relaxation in inhomogeneous quantum quenches allows to compute asymptotically the expectation value of local observables via hydrodynamic arguments known as generalized hydrodynamics (GHD). In this work we address…

While $1+1$ dimensional growth models in the Kardar-Parisi-Zhang universality class have witnessed an explosion of activity, higher dimensional models remain much less explored. The special case of $2+1$ dimensions is particularly…

We establish the existence, uniqueness and attraction properties of an ergodic invariant measure for the Boussinesq Equations in the presence of a degenerate stochastic forcing acting only in the temperature equation and only at the largest…

In this work we present scattering functions of conjugates consisting of a colloid particle and a self-avoiding polymer chain. This model is directly derived from the two point correlation function with the inclusion of excluded volume…

We address the six vertex model on a random lattice, which in combinatorial terms corresponds to the enumeration of weighted 4-valent planar maps equipped with an Eulerian orientation. This problem was exactly, albeit non-rigorously solved…

For a cycle of codimension 1 in a toric variety, its degree with respect to a nef toric divisor can be understood in terms of the mixed volume of the polytopes associated to the divisor and to the cycle. We prove here that an analogous…

Motivated by recent work on studying massive imaging data in various neuroimaging studies, we propose a novel spatially varying coefficient model (SVCM) to spatially model the varying association between imaging measures in a…

We introduce a stochastic agent-based model for the flocking dynamics of self-propelled particles that exhibit velocity-alignment interactions with neighbours within their field of view. The stochasticity in the dynamics of the model arises…

A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is…

Covariance functions are the core of spatial statistics, stochastic processes, machine learning as well as many other theoretical and applied disciplines. The properties of the covariance function at small and large distances determine the…

It was recently shown that multi-point conformal blocks in higher dimensional conformal field theory can be considered as joint eigenfunctions for a system of commuting differential operators. The latter arise as Hamiltonians of a Gaudin…

A self-consistent projection operator method for single-particle excitations is developed. It describes the nonlocal correlations on the basis of a projection technique to the retarded Green function and the off-diagonal effective medium.…

We study two models of discrete height functions, that is, models of random integer-valued functions on the vertices of a tree. First, we consider the random homomorphism model, in which neighbours must have a height difference of exactly…

We extend a class of recently derived thermodynamic uncertainty relations to vector-valued observables. In contrast to the scalar-valued observables examined previously, this multidimensional thermodynamic uncertainty relation provides a…

We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schr\"{o}dinger (DNLS) equations with the attractive self-phase-modulation (SPM) nonlinearity, coupled…

Using the fermionic basis discovered in the 6-vertex model, we derive exact formulas for the expectation values of local operators of the sine-Gordon theory in any eigenstate of the Hamiltonian. We tested our formulas in the pure…

Scalable general-purpose representations of the built environment are crucial for geospatial artificial intelligence applications. This paper introduces S2Vec, a novel self-supervised framework for learning such geospatial embeddings. S2Vec…

This article introduces a dynamic spatiotemporal stochastic volatility (SV) model with explicit terms for the spatial, temporal, and spatiotemporal spillover effects. Moreover, the model includes time-invariant site-specific constant…

We study a class of close-packed dimer models on the square lattice, in the presence of small but extensive perturbations that make them non-determinantal. Examples include the 6-vertex model close to the free-fermion point, and the dimer…