相关论文: Renormalization analysis of catalytic Wright-Fishe…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
In this work, we develop excursion theory for the Wright--Fisher diffusion with mutation. Our construction is intermediate between the classical excursion theory where all excursions begin and end at a single point and the more general…
Renormalization Group flows relate the values of couplings at different scales. Here, we go beyond the Renormalization Group flow of individual trajectories and derive an evolution equation for a distribution on the space of couplings. This…
Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's…
We study the renormalization group flow of $\mathbb{Z}_2$-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention to the fixed…
A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures.…
The stationary distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree to…
We prove that the generator of the renormalization group of Potts models on hierarchical lattices can be represented by a rational map acting on a finite-dimensional product of complex projective spaces. In this framework we can also…
Diffusion with an incorporated resetting mechanism provides a reference framework for modeling a wide range of natural phenomena. Within this framework, the optimal resetting rate is a key quantity that arises from the optimization of the…
We consider a one-parameter family of piecewise isometries of a rhombus. The rotational component is fixed, and its coefficients belong to the quadratic number field $K=\mathbb{Q}(\sqrt{2})$. The translations depend on a parameter $s$ which…
Our motivation comes from the large population approximation of individual based models in population dynamics and population genetics. We propose a general method to investigate scaling limits of finite dimensional population size Markov…
The global-in-time existence of renormalized solutions to reaction-cross-diffu-sion systems for an arbitrary number of variables in bounded domains with no-flux boundary conditions is proved. The cross-diffusion part describes the…
The Wright--Fisher diffusion is important in population genetics in modelling the evolution of allele frequencies over time subject to the influence of biological phenomena such as selection, mutation, and genetic drift. Simulating paths of…
Characterizing time-evolution of allele frequencies in a population is a fundamental problem in population genetics. In the Wright-Fisher diffusion, such dynamics is captured by the transition density function, which satisfies well-known…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
Wright-Fisher diffusions describe the evolution of the type composition of an infinite haploid population with two types (say type $0$ and type $1$) subject to neutral reproductions, and possibly selection and mutations. In the present…
The renormalization procedure is proved to be a rigorous way to get finite answers in a renormalizable class of field theories. We claim, however, that it is redundant if one reduces the requirement of finiteness to S-matrix elements only…
It is known that the time until a birth and death process reaches a certain level is distributed as a sum of independent exponential random variables. Diaconis, Miclo and Swart gave a probabilistic proof of this fact by coupling the birth…
We study a generalization of the Wright--Fisher model in which some individuals adopt a behavior that is harmful to others without any direct advantage for themselves. This model is motivated by studies of spiteful behavior in nature,…
The eigenfunction expansion by Gegenbauer polynomials for the diffusion on a hypersphere is transformed into the diffusion for the Wright-Fisher model with a particular mutation rate. We use the Ito calculus considering stochastic…