Related papers: Local Stability of the Free Additive Convolution
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
We develop a stability theory for contractive local IFSs on compact metric spaces. Unlike the classical global setting, local systems may exhibit a richer symbolic and geometric structure, including code spaces that are not of finite type…
We show that in the system of two fermions interacting by scalar exchange, the solutions for J$^{\pi}$=$0^+$ bound states are stable without any cutoff regularization, for values of the coupling constant $\alpha$ below a critical value…
A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit…
Regularization methods have been recently developed to construct stable approximate solutions to classical partial differential equations considered as final value problems. In this paper, we investigate the backward parabolic problem with…
In the presence of persistent payoff heterogeneity, the evolution of the aggregate strategy hugely depends on the underlying strategy composition under many evolutionary dynamics, while the aggregate dynamic under the standard BRD reduces…
For three-dimensional piecewise-smooth systems of ordinary differential equations, this paper characterises the stability of points that belong to a switching surface and are equilibria of exactly one of the two neighbouring pieces of the…
We consider discrete-time switching systems composed of a finite family of affine sub-dynamics. First, we recall existing results and present further analysis on the stability problem, the existence and characterization of compact…
We study localizations (in the sense of J. L. Taylor) of the universal enveloping algebra, U(g), of a complex Lie algebra g. Specifically, let f : U(g) --> H be a homomorphism to some well-behaved topological Hopf algebra H. We formulate…
Stochastic hybrid inclusions (SHIs) address situations with the stochastic continuous evolution in a stochastic differential inclusions and random jumps in the difference inclusions due to the forced (the state reaching a boundary in the…
Let $\mu$ and $\nu$ be probability measures on $\mathbb{R}$ with compact support, and let $\mu \boxplus \nu$ denote their additive free convolution. We show that for $z \in \mathbb{R}$ greater than the sum of essential suprema of $\mu$ and…
We prove several new results on the absolutely continuous spectra of perturbed one-dimensional Stark operators. First, we find new classes of perturbations, characterized mainly by smoothness conditions, which preserve purely absolutely…
We introduce and study a new type of convolution of probability measures called the orthogonal convolution, which is related to the monotone convolution. Using this convolution, we derive alternating decompositions of the free additive…
Statistical independence is a notion ubiquitous in various fields such as in statistics, probability, number theory and physics. We establish the stability of independence for any pair of random variables by their corresponding Brockwell…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
Let \Lambda be a finite subset of Z^d. We study the following sandpile model on \Lambda. The height at any given vertex x of \Lambda is a positive real number, and additions are uniformly distributed on some interval [a,b], which is a…
We approach string phenomenology from the perspective of computational algebraic geometry, by providing new and efficient techniques for proving stability and calculating particle spectra in heterotic compactifications. This is done in the…
Many natural Markov chains fail to mix to their stationary distribution in polynomially many steps. Often, this slow mixing is inevitable since it is computationally intractable to sample from their stationary measure. Nevertheless, Markov…
We consider the aggregation equation $u_t= \div(\nabla u-u\nabla \K(u))$ in a bounded domain $\Omega\subset \R^d$ with supplemented the Neumann boundary condition and with a nonnegative, integrable initial datum. Here, $\K=\K(u)$ is an…
We develop analytic tools for studying the free multiplicative convolution of any measure on the real line and any measure on the nonnegative real line. More precisely, we construct the subordination functions and the $S$-transform of an…