相关论文: Renormalization analysis of catalytic Wright-Fishe…

The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first…

Flux reconstruction provides a framework for solving partial differential equations in which functions are discontinuously approximated within elements. Typically, this is done by using polynomials. Here, the use of radial basis functions…

We develop a new renormalization group approach to the large-N limit of matrix models. It has been proposed that a procedure, in which a matrix model of size (N-1) \times (N-1) is obtained by integrating out one row and column of an N…

We consider infinitely renormalizable unimodal mappings with topological type which is periodic under renormalization. We study the limiting behavior of fixed points of the renormalization operator as the order of the critical point…

We develop a renormalization theory for analytic homeomorphisms of the circle with two cubic critical points. We prove a renormalization hyperbolicity theorem. As a basis for the proofs, we develop complex a priori bounds for multi-critical…

As a class of generative artificial intelligence frameworks inspired by statistical physics, diffusion models have shown extraordinary performance in synthesizing complicated data distributions through a denoising process gradually guided…

We investigate the properties of a Wright-Fisher diffusion process started from frequency x at time 0 and conditioned to be at frequency y at time T. Such a process is called a bridge. Bridges arise naturally in the analysis of selection…

We consider diffusion processes x_{t} on the unit interval. Doob-transformation techniques consist of a selection of x_{t}-paths procedure. The law of the transformed process is the one of a branching diffusion system of particles, each…

Gradient flow has proved useful in the definition and measurement of renormalized quantities on the lattice. Recently, the fact that it suppresses high-modes of the field has been used to construct new, continuous RG transformations both…

Power corrections to exclusive processes are usually calculated using models for twist-four distribution amplitudes (DA) which are based on the leading-order terms in the conformal expansion. In this work we develop a different approach…

We study renormalization-group flows in Yukawa theories with massless fermions, including determination of fixed points and curves that separate regions of different flow behavior. We assess the reliability of perturbative calculations for…

The problem of the lattice diffusion of two particles coupled by a contact repulsive interaction is solved by finding analytical expressions of the two-body probability characteristic function. The interaction induces anomalous drift with a…

Normalizing Flows (NFs) are a classical family of likelihood-based methods that have received revived attention. Recent efforts such as TARFlow have shown that NFs are capable of achieving promising performance on image modeling tasks,…

We present an extension of the previously proposed mean-field renormalization method to model Hamiltonians which are characterized by more than just one type of interaction. The method rests on scaling assumptions about the magnetization of…

The non-perturbative renormalization-group approach is extended to lattice models, considering as an example a $\phi^4$ theory defined on a $d$-dimensional hypercubic lattice. Within a simple approximation for the effective action, we solve…

Modern reinforcement learning (RL) algorithms have found success by using powerful probabilistic models, such as transformers, energy-based models, and diffusion/flow-based models. To this end, RL researchers often choose to pay the price…

We develop a renormalization group for weak Harris-marginal disorder in otherwise strongly interacting quantum critical theories, focusing on systems which have emergent conformal invariance. Using conformal perturbation theory, we argue…

A general framework is presented for the renormalization of Hamiltonians via a similarity transformation. Divergences in the similarity flow equations may be handled with dimensional regularization in this approach, and the resulting…

We study two dimensional freely decaying magnetohydrodynamic turbulence. We investigate the time evolution of the probability law of the gauge field and the stream function. Assuming that this probability law is initially defined by a…

We study a class of processes that are akin to the Wright-Fisher model, with transition probabilities weighted in terms of the frequency-dependent fitness of the population types. By considering an approximate weak formulation of the…