Related papers: Modelling gap-size distribution of parked cars usi…
Modeling of headway/spacing between two consecutive vehicles has many applications in traffic flow theory and transport practice. Most known approaches only study the vehicles running on freeways. In this paper, we propose a model to…
We show that the spacing distribution between parked cars can be obtained as a solution of certain linear distributional fixed point equation. The results are compared with the data measured on the streets of Hradec Kralove. We also discuss…
Models of parking in which cars are placed randomly and then move according to a deterministic rule have been studied since the work of Konheim and Weiss in the 1960s. Recently, Damron, Gravner, Junge, Lyu, and Sivakoff introduced a model…
In this paper, we explore parking distributions on caterpillar trees, focusing on two primary statistics: the number of lucky cars and the frequency with which cars prefer specific parking spaces. We use first-return decomposition to reveal…
We derive the exact formula for thermal-equilibrium spacing distribution of one-dimensional particle gas with repulsive potential V(r)=r^(-a) (a>0) depending on the distance r between the neighboring particles. The calculated distribution…
It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special…
We investigate a microscopical structure in a chain of cars waiting at a red signal on signal-controlled crossroads. Presented is an one-dimensional space-continuous thermodynamical model leading to an excellent agreement with the data…
We performed extensive simulations accompanied by a detailed study of a two-segment size random sequential model on the line. We followed the kinetics towards the jamming state, but we paid particular attention to the characterization of…
We consider the system of particles with equal charges and nearest neighbour Coulomb interaction on the interval. We study local properties of this system, in particular the distribution of distances between neighbouring charges. For zero…
Consider sequential packing of unit balls in a large cube, as in the Renyi car-parking model, but in any dimension and with Poisson input. We show after suitable rescaling that the spatial distribution of packed balls tends to that of a…
We describe an ensemble of (sparse) random matrices whose eigenvalues follow the Gibbs distribution for n particles of the Coulomb gas on the unit circle at inverse temperature beta. Our approach combines elements from the theory of…
We study the non-asymptotic behavior of Coulomb gases in dimension two and more. Such gases are modeled by an exchangeable Boltzmann-Gibbs measure with a singular two-body interaction. We obtain concentration of measure inequalities for the…
An asymmetric exclusion process type process, where cars move forward along a closed road that starts and terminates at a parking garage, displays dynamic phase transitions into two types of condensate phases where the garage becomes…
A random matrix representation is proposed for the two-dimensional (2D) Coulomb gas at inverse temperature $\beta$. For $2\times 2$ matrices with Gaussian distribution we analytically compute the nearest neighbour spacing distribution of…
The parking issue is central in transport policies and drivers' concerns, but the determinants of the parking search time remain relatively poorly understood. The question is often handled in a fairly ad hoc way, or by resorting to crude…
In the classical parking problem, unit intervals ("car lengths") are placed uniformly at random without overlapping. The process terminates at saturation, i.e. until no more unit intervals can be stowed. In this paper, we present a…
In this article, we establish new results on the probabilistic parking model (introduced by Durm\'ic, Han, Harris, Ribeiro, and Yin) with $m$ cars and $n$ parking spots and probability parameter $p\in[0,1]$. For any $ m \leq n$ and $p \in…
Random-matrix theory is used to study the mesoscopic fluctuations of the excitation gap in a metal grain or quantum dot induced by the proximity to a superconductor. We propose that the probability distribution of the gap is a universal…
Universality of local eigenvalue statistics is one of the most striking phenomena of Random Matrix Theory, that also accounts for a lot of the attention that the field has attracted over the past 15 years. In this paper we focus on the…
Invariant ensemble, which are characterised by the joint distribution of eigenvalues $P(\lambda_1,\ldots,\lambda_N)$, play a central role in random matrix theory. We consider the truncated linear statistics $L_K = \sum_{n=1}^K f(\lambda_n)$…