Related papers: Series expansion for a stochastic sandpile
We show, within the framework of the Euclidean $\phi^4$-quantum field theory in four dimensions, that the Wilson operator product expansion (OPE) is not only an asymptotic expansion at short distances as previously believed, but even…
It has been recently proposed to use the operator product expansion to evaluate the expectation values of renormalized operators without the need of a direct computation of the relevant renormalization constants. We test the viability of…
We study the dynamics of the Stochastic Sandpile Model on finite graphs, with two main results. First, we describe a procedure to exactly sample from the stationary distribution of the model in all connected finite graphs, extending a…
We analyze the properties of a class of improved lattice topological charge density operators, constructed by a smearing-like procedure. By optimizing the choice of the parameters introduced in their definition, we find operators having (i)…
In the stochastic sandpile model on a graph, particles interact pairwise as follows: if two particles occupy the same vertex, they must each take an independent random walk step with some probability $0<p<1$ of not moving. These…
New extra series of conserved densities for the polytropic gas model and nonlinear elasticity equation are obtained without any references to the recursion operator or to the Lax operator formalism. Our method based on the utilization of…
Neural operator (NO) architectures learn nonlinear maps between infinite-dimensional function spaces and are widely used to accelerate simulation and enable data-driven model discovery. While universality results ensure expressivity, they…
We use series expansions to study dynamics of equilibrium and non-equilibrium systems on networks. This analytical method enables us to include detailed non-universal effects of the network structure. We show that even low order…
Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PD's) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in…
Recently an expansion as a power series in 1/d has been presented for the specific entropy of a complete dimer covering of a d-dimensional hypercubic lattice. This paper extends from 3 to 10 the number of terms known in the series. Likewise…
We investigate operator delocalization in disordered one-dimensional spin chains by introducing -- besides the already known operator mass -- a complementary measure of operator complexity: the operator length. Like the operator…
We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the…
We consider a recursive scheme for defining the coefficients in the operator product expansion (OPE) of an arbitrary number of composite operators in the context of perturbative, Euclidean quantum field theory in four dimensions. Our…
The paper examines the construction and analysis of a new class of mixed exponential statistical structures that combine the properties of stochastic models and linear positive operators. The relevance of the topic is driven by the growing…
We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around…
A general class of dynamical systems which can be trained to operate in classification and generation modes are introduced. A procedure is proposed to plant asymptotic stationary attractors of the deterministic model. Optimizing the…
We provide an ergodic theorem for certain Banach-space valued functions on structures over $\ZZ^d$, which allow for existence of frequencies of finite patterns. As an application we obtain existence of the integrated density of states for…
There are many results on the simultaneous approximation by sequences of special positive linear operators. In the year 1978, Ismail and May as well as Volkov independently studied operators of exponential type covering the most classical…
We study a one-dimensional fixed-energy version (that is, with no input or loss of particles), of Manna's stochastic sandpile model. The system has a continuous transition to an absorbing state at a critical value $\zeta_c$ of the particle…
Conditional density estimation (CDE) models can be useful for many statistical applications, especially because the full conditional density is estimated instead of traditional regression point estimates, revealing more information about…