Related papers: Equilibrium states for potentials with $\sup\phi -…
The subleading eigenvalues and associated eigenfunctions of the Perron-Frobenius operator for 2-dimensional area-preserving maps are numerically investigated. We closely examine the validity of the so-called Ulam method, a numerical scheme…
Partial summing of infinite range of diagrams for the two-phonon mass operator of polaron described by Fr\"{o}hlich Hamiltonian is performed using the Feynman-Pines diagram technique. Renormalized spectral parameters of ground and first…
We prove an optimal semiclassical bound on the trace norm of the following commutators $[\boldsymbol{1}_{(-\infty,0]}(H_\hbar),x]$, $[\boldsymbol{1}_{(-\infty,0]}(H_\hbar),-i\hbar\nabla]$ and…
We propose an experimentally accessible scheme to determine lower bounds on the quantum Fisher information (QFI), which ascertains multipartite entanglement or usefulness for quantum metrology. The scheme is based on comparing the…
Consider a finite absorbing Markov generator, irreducible on the non-absorbing states. Perron-Frobenius theory ensures the existence of a corresponding positive eigenvector $\varphi$. The goal of the paper is to give bounds on the amplitude…
Let $(X,d)$ be a compact metric space, $f:X \mapsto X$ be a continuous map with the specification property, and $\varphi: X \mapsto \IR$ a continuous function. We consider the set of points for which the Birkhoff average of $\varphi$ does…
We propose an inverse approach for dealing with interval maps based on the manner whereby their branches are related (folding property), instead of addressing the map equations as a whole. As a main result, we provide a symmetry-breaking…
We prove that for every locally stable and tempered pair potential $\phi$ with bounded range, there exists a unique infinite-volume Gibbs point process on $\mathbb{R}^d$ for every activity $\lambda < (e^{L} \hat{C}_{\phi})^{-1}$, where $L$…
We prove local limit theorems for mod-{\phi} convergent sequences of random variables, {\phi} being a stable distribution. In particular, we give two new proofs of a local limit theorem in the framework of mod-phi convergence: one proof…
There has been significant developments in the classification of boundary conditions of positive symmetric systems, also known as Friedrichs systems, after the introduction of operator theoretic framework. We take a step forward towards…
In this work we propose a new analytical method for determining the scalar field potential $V(\phi)$ in FRW type cosmologies containing a mixture of perfect fluid plus a quintessence scalar field. By assuming that the equation of state…
Simultaneous estimation of multiple parameters is required in many practical applications. A lower bound on the variance of simultaneous estimation is given by the quantum Fisher information matrix. This lower bound is, however, not…
The parabolic-elliptic Keller-Segel equation with sensitivity saturation, because of its pattern formation ability, is a challenge for numerical simulations. We provide two finite-volume schemes whose goals are to preserve, at the discrete…
Conditions are derived on line-of-sight channels to ensure the feasibility of interference alignment. The conditions involve choosing only the spacing between two subcarriers of an orthogonal frequency division multiplexing (OFDM) scheme.…
Let $X$ be a stationary process with finite state-space $A$. Bressaud et al. recently provided a sufficient condition for the natural filtration of $X$ to be standard when $A$ has size 2. Their condition involves the conditional laws…
We analyze a problem of optimal control of the Fokker-Planck equation with state constraints in the Wasserstein space of probability measures. Our main result is to derive optimality conditions in the form of a Mean Field Game system of…
We prove sharp upper bounds for eigenvalues of Schr\"odinger operators on quantum graphs with $\delta$-coupling (also known as Robin) conditions at all vertices. The bounds depend on the geometry of the graph, on the potential, and the…
Consider a topologically transitive countable Markov shift $\Sigma$ and a summable Markov potential $\phi$ with finite Gurevich pressure and $\mathrm{Var}_1(\phi) < \infty$. We prove existence of the limit $\lim_{t \to \infty} \mu_t$ in the…
We consider the problem of overbounding and underbounding both the backward and forward reachable set for a given polynomial vector field, nonlinear in both state and input, with a given semialgebriac set of initial conditions and with…
We prove two lower bounds for the complexity of non-log-concave sampling within the framework of Balasubramanian et al. (2022), who introduced the use of Fisher information (FI) bounds as a notion of approximate first-order stationarity in…