arXiv subjects

Jiaojiao Yang

Publications and source records attributed to Jiaojiao Yang.

4 recordsLinked to original sources

arXiv2026

Wave propagation for 1-dimensional reaction-diffusion equations with nonzero random drift

We consider the wave propagation for a reaction-diffusion equation on the real line, with a random drift and Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) type nonlinear reaction. We show that when the average drift is positive, the asymptotic wave fronts propagating to the positive and negative directions are both pushed in the negative direction, leading to the possibility that both wave fronts propagate toward negative infinity. Our proof is based on the Large Deviations Principle for diffusion processes in random environments, as well as an analysis of the Feynman-Kac formula. Such probabilistic arguments also reveal the underlying physical mechanism of the wave fronts formation: the drift acts as an external field that shifts the (quenched) free-energy reference level without altering the intrinsic fluctuation structure of the system.

math.AP↗

arXiv2024

Quasisymmetric minimality on packing dimension for homogeneous perfect sets

In this paper, we study the quasisymmetric packing minimality of homogeneous perfect sets, and obtain that a special class of homogeneous perfect sets with $\operatorname{dim}_{P}E=1$ is quasisymmetrically packing minimal.

math.GN↗

arXiv2020

On the fast convergence of random perturbations of the gradient flow

We consider in this work small random perturbations (of multiplicative noise type) of the gradient flow. We prove that under mild conditions, when the potential function is a Morse function with additional strong saddle condition, the perturbed gradient flow converges to the neighborhood of local minimizers in $O(\ln (\varepsilon^{-1}))$ time on the average, where $\varepsilon$ is the scale of the random perturbation. Under a change of time scale, this indicates that for the diffusion process that approximates the stochastic gradient method, it takes (up to logarithmic factor) only a linear time of inverse stepsize to evade from all saddle points. This can be regarded as a manifestation of fast convergence of the discrete-time stochastic gradient method, the latter being used heavily in modern statistical machine learning.

math.PR↗

arXiv2017

A note on correlation and local dimensions

Under very mild assumptions, we give formulas for the correlation and local dimensions of measures on the limit set of a Moran construction by means of the data used to construct the set.

math.CA↗