Related papers: Stein's method and approximating the multidimensio…
We explore two aspects of geometric approximation via a coupling approach to Stein's method. Firstly, we refine precision and increase scope for applications by convoluting the approximating geometric distribution with a simple translation…
This survey article discusses the main concepts and techniques of Stein's method for distributional approximation by the normal, Poisson, exponential, and geometric distributions, and also its relation to concentration inequalities. The…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
We develop Stein's method for the half-normal distribution and apply it to derive rates of convergence in distributional limit theorems for three statistics of the simple symmetric random walk: the maximum value, the number of returns to…
We derive upper bounds on the Wasserstein distance ($W_1$), with respect to $\sup$-norm, between any continuous $\mathbb{R}^d$ valued random field indexed by the $n$-sphere and the Gaussian, based on Stein's method. We develop a novel…
The quasiprobability distribution of the discrete Wigner function provides a complete description of a quantum state and is, therefore, a useful alternative to the usual density matrix description. Moreover, the experimental quantum state…
The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. Here, we introduce the concept of an "eigenstate witness" and through it…
Using a characterizing equation for the Beta distribution, Stein's method is applied to obtain bounds of the optimal order for the Wasserstein distance between the distribution of the scaled number of white balls drawn from a…
Variance-Gamma distributions are widely used in financial modelling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein's method to this class of distributions. In particular, we obtain a…
We consider the following second-order stochastic differential equation on $\mathbb{R}^{2d}$: \begin{equation*} dX_t^m=Y_t^mdt, \quad mdY_t^m=b(X_t^m)dt+\sigma(X_t^m)dB_t-Y^m_tdt, \end{equation*} where $X^m_t$ and $Y^m_t$ represent the…
From its beginning, there have been attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the…
Random events in space and time often exhibit a locally dependent structure. When the events are very rare and dependent structure is not too complicated, various studies in the literature have shown that Poisson and compound Poisson…
Stein's method is used to obtain two theorems on multivariate normal approximation. Our main theorem, Theorem 1.2, provides a bound on the distance to normality for any nonnegative random vector. Theorem 1.2 requires multivariate size bias…
We show how multi-level BCS Hamiltonians of finite systems in the strong pairing interaction regime can be accurately approximated using multi-dimensional shifted harmonic oscillator Hamiltonians. In the Shifted Harmonic Approximation…
Quantum ground-state problems are computationally hard problems; for general many-body Hamiltonians, there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating…
Starting from the study of one-dimensional potentials in quantum mechanics having a small distance behavior described by a harmonic oscillator, we extend this way of analysis to models where such a behavior is not generally expected. In…
We show how the use of variational states to approximate the ground state of a system can be employed to study a multi-mode Dicke model. One of the main contributions of this work is the introduction of a not very commonly used quantity,…
Many spatial models exhibit locality structures that effectively reduce their intrinsic dimensionality, enabling efficient approximation and sampling of high-dimensional distributions. However, existing approximation techniques primarily…
A two-step optimization is proposed to represent an arbitrary quantum state to a desired accuracy with the least number of gaussians in phase space. The Husimi distribution of the quantum state provides the information to determine the…
If $\mathbb{Y}$ is a random vector in $\mathbb{R}^{d}$, we denote by $P_{\mathbb{Y}}$ its probability distribution. Consider a random variable $X$ and a $d$-dimensional random vector $\mathbb{Y}$. Inspired by \cite{Pi}, we develop a…