Related papers: The renormalization transformation for two-type br…
We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…
This work continues and substantially extends our recent work on switching diffusions with the switching processes that depend on the past states and that take values in a countable state space. That is, the discrete components of the…
Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized reactions in the continuum limit. Here, various non-local interactions are considered, and two…
Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…
Different branching and annihilating random walk models are investigated by cluster mean-field method and simulations in one and two dimensions. In case of the A -> 2A, 2A -> 0 model the cluster mean-field approximations show diffusion…
Far from equilibrium, neural systems self-organize across multiple scales. Exploiting multiscale self-organization in neuroscience and artificial intelligence requires a computational framework for modeling the effective non-equilibrium…
Diffusion models represent a class of generative models that produce data by denoising a sample corrupted by white noise. Despite the success of diffusion models in computer vision, audio synthesis, and point cloud generation, so far they…
We consider a system of interacting diffusions labeled by a geographic space that is given by the hierarchical group $\Omega_N$ of order $N\in\mathbb{N}$. Individuals live in colonies and are subject to resampling and migration as long as…
We analyze a semi-infinite one-dimensional random walk process with a biased motion that is incremental in one direction and long-range in the other. On a network with a fixed hierarchy of long-range jumps, we find with exact…
Recently, several authors have studied maps where a function, describing the local diffusion matrix of a diffusion process with a linear drift towards an attraction point, is mapped into the average of that function with respect to the…
It is shown by the method of renormalized field theory that in contrast to a statement based on a mathematically ill-defined invariance transformation and found in most of the recent publications on growth models with surface diffusion, the…
We study a class of reaction-diffusion model extrapolating continuously between the pure coagulation-diffusion case ($A+A\to A$) and the pure annihilation-diffusion one ($A+A\to\emptyset$) with particles input ($\emptyset\to A$) at a rate…
We investigate non-equilibrium critical phenomena using a nonperturbative renormalization group method. Reaction-diffusion processes are described by a scale dependent effective action which evolution is governed by very generic flow…
We investigate a class of continuum models for the motion of a two-dimensional biological group under the influence of nonlocal social interactions. The dynamics may be uniquely decomposed into incompressible motion and potential motion.…
An asymmetric variant of the contact process where the activity spreads with different and independent random rates to the left and to the right is introduced. A real space renormalization scheme is formulated for model by means of which it…
We present a field theoretic renormalization group study for the critical behaviour of a uniformly driven diffusive system with quenched disorder, which is modelled by different kinds of potential barriers between sites. Due to their…
We consider a system of random walks in a random environment interacting via exclusion. The model is reversible with respect to a family of disordered Bernoulli measures. Assuming some weak mixing conditions, it is shown that, under…
Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical…
We describe an extension to the density matrix renormalization group method incorporating real time evolution into the algorithm. Its application to transport problems in systems out of equilibrium and frequency dependent correlation…
In this paper, we introduce new reference observables to establish a scaling formula in the renormalization group equation. Using the transfer matrix method, we calculate the two point observables of the one dimensional Ising model without…