Related papers: Gaussian fluctuations for the two urn model
A model based on the classic non-interacting Ehrenfest urn model with two-urns is generalized to $M$ urns with the introduction of interactions for particles within the same urn. As the inter-particle interaction strength is varied, phases…
We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue…
We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions subject to projective monitoring of local charge across the measurement-induced phase transition. Our observables are…
Using P\'{o}lya's urn model with negative replacement we introduce a new Bernstein-type operator and we show that the new operator improves upon the known estimates for the classical Bernstein operator. We also provide numerical evidence…
We investigate the bifurcation phenomena for stochastic systems with multiplicative Gaussian noise, by examining qualitative changes in mean phase portraits. Starting from the Fokker-Planck equation for the probability density function of…
Let $U$ be a Haar distributed matrix in $\mathbb U(n)$ or $\mathbb O (n)$. In a previous paper, we proved that after centering, the two-parameter process \[T^{(n)} (s,t) = \sum_{i \leq \lfloor ns \rfloor, j \leq \lfloor nt\rfloor}…
We present arguments in favour of the inequalities $var(X_n^2|X \in B_v(\rho)) \le 2\lambda_n E[X_n^2|X \in B_v(\rho)]$, where $X \sim N_v(0,\Lambda)$ is a normal vector in $v\ge 1$ dimensions, with zero mean and covariance matrix $\Lambda…
The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order…
Smooth linear statistics of random permutation matrices, sampled under a general Ewens distribution, exhibit an interesting non-universality phenomenon. Though they have bounded variance, their fluctuations are asymptotically non-Gaussian…
Linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems. The proofs of such results are usually rather difficult, involving hard computations specific to the model in…
Dynamical urn models, such as the Ehrenfest model, have played an important role in the early days of statistical mechanics. Dynamical many-urn models generalize the former models in two respects: the number of urns is macroscopic, and…
In this paper, we analyze the random fluctuations in a one dimensional stochastic homogenization problem and prove a central limit result, i.e., the first order fluctuations can be described by a Gaussian process that solves an SPDE with…
The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a…
We consider the effect of volume fluctuations on cumulants of the net baryon number. Based on a general formalism, we derive universal expressions for the net baryon number cumulants in the presence of volume fluctuations with an arbitrary…
We show that as $n$ changes, the characteristic polynomial of the $n\times n$ random matrix with i.i.d. complex Gaussian entries can be described recursively through a process analogous to P\'olya's urn scheme. As a result, we get a random…
We study stationary fluctuations of conserved slow modes in a two-lane model of hardcore particles which are expected to show universal behaviour. Specifically, we focus on the properties of fluctuations at a special umbilic point where the…
We generalize and extend the recently proposed method to account for contributions of system size (or volume/participant) fluctuations to the experimentally measured moments of particle multiplicity distributions. We find that in the…
We consider multicolor urn models with multiple drawings. An urn model is called linear if the conditional expected value of the urn composition at time $n$ is a linear function of the composition at time $n-1$. For four different sampling…
We review two recent results on the ground state properties of bosonic systems trapped by a double well external potential. In the limit of large population and large separation between the wells we prove that fluctuations in the number of…
For the plain Polya urn with two colors, black and white, we prove a functional central limit theorem for the number of white balls assuming that the initial number of black balls is large. Depending on the initial number of white balls,…