2 citations · 3 across the 10 of their papers we have counts for
10 papers
Quantitative propagation of chaos for the Boltzmann equation with moderately soft potentials
Chenguang Liu, Liping Xu, An Zhang
We study the Kac particle system associated with the spatially homogeneous Boltzmann equation with non-cutoff collision kernels in the moderately soft potential regime . We…
Strichartz estimates for orthonormal systems on compact manifolds: the non-sharp region
Hongzhou Ji, Liping Xu, An Zhang
We establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the non-sharp admissible region of exponents, covering wave, Klein-Gordon, and frac…
Central limit theorem for a partially observed interacting system of Hawkes processes I: subcritical case
Chenguang Liu, Liping Xu, An Zhang
We consider a system of Hawkes processes and observe the actions of a subpopulation of size up to time , where is large. The influence relationships between ea…
Scaling limit for supercritical nearly unstable Hawkes processes with heavy tail
Liping Xu, An Zhang
In this paper, we establish the asymptotic behavior of {\it supercritical} nearly unstable Hawkes processes with a power law kernel. We find that, the Hawkes process in our context…
Rate of convergence of the Kac particle system for the Boltzmann equation with hard potentials
Chenguang Liu, Liping Xu, An Zhang
In this paper, we prove that the Kac stochastic particle system converges to the weak solution of the spatially homogeneous Boltzmann equation for hard potentials and hard spheres.…
Scaling limits for supercritical nearly unstable Hawkes processes
Chenguang Liu, Liping Xu, An Zhang
In this paper, we investigate the asymptotic behavior of nearly unstable Hawkes processes whose regression kernel has norm strictly greater than one and close to one as time…
Rate of convergence of the Kac-like particle system
Chenguang Liu, Liping Xu
In this paper, we consider the Kac stochastic particle system associated to the spatially homogeneous Boltzmann equation for true hard potentials. We establish a rate of propagatio…
On the equivalence between some jumping SDEs with rough coefficients and some non-local PDEs
Nicolas Fournier, Liping Xu
We study some jumping SDE and the corresponding Fokker-Planck (or Kolmogorov forward) equation, which is a non-local PDE. We assume only some measurability and growth conditions on…
Uniqueness and propagation of chaos for the Boltzmann equation with moderately soft potentials
Liping Xu
We prove a strong/weak stability estimate for the 3D homogeneous Boltzmann equation with moderately soft potentials () using the Wasserstein distance with quadratic cos…
The Multifractal Nature of Boltzmann Processes
Liping Xu
We consider the spatially homogeneous Boltzmann equation for (true) hard and moderately soft potentials. We study the pathwise properties of the stochastic process $(V_t)_{t\geq 0}…