arXiv subjects

Sanjoy Kumar Jhawar

Publications and source records attributed to Sanjoy Kumar Jhawar.

6 recordsLinked to original sources

arXiv2026

On a Class of Dynamical Poisson-Voronoi Tessellations

Consider a dynamical network model featuring mobile stations on the Euclidean plane. The initial locations of the stations are given by a homogeneous Poisson point process. The stations are all moving at a constant speed and in a random direction. Consider fixed users located in the Euclidean plane, which are served by the mobile stations. Each user stays connected to the nearest station at any given point of time. Since the stations are moving, a user disconnects and connects with different stations over time, by always selecting which ever station is the closest. This gives rise to a dynamical version of the Poisson-Voronoi tessellation. The focus of this paper is on the sequence of ``handover'' events of a typical user, which are the epochs when its association changes. This defines a point process on the time-axis, the ``handover point process''. We show that this point process is stationary and we determine its main properties, in particular its intensity and the joint distribution of its inter-event times. We also analyze the handover Palm distributions of several variables of practical interest. This includes the distance to the closest mobile stations and the point process of all other mobile stations at handover epochs. The analysis is conducted both in the single-speed and in the multi-speed scenarios. Closed form expressions are obtained in both cases. It leads to the identification of the three dimensional state variables that ``Markovize'' the association dynamics. The analysis is based on a specific system of non-compact particles. The motivations are in the modeling of low or medium orbit satellite wireless communication networks. The model studied here is a planar ``caricature'' of this problem, which is initially defined on the sphere.

math.PR↗

arXiv2026

Seasonal Statistics of Shannon Rate in a Dynamical Poisson-Voronoi Cellular Network

In this work we consider a dynamical cellular communication network in which mobile base stations (BSs) are modeled as a homogeneous Poisson point process on $\mathbb{R}^2$. Each base station moves at a constant speed in a random direction. A typical user connects to the nearest base station and it experiences variable signal and interference powers depending on the distance of all the stations. Along the motion of the stations, the user swaps its serving station, and such an event is called a {\em handover}. We are interested in the performance evaluation of the system under some classical and tropical metrics of interest at different time of events, inducing handovers, maximal proximity of serving station, nearest interferer at closest or farthest distance with respect to the user or at any typical time epoch. The main results of the paper are closed or integral form expressions for the basic metrics of interest, in particular coverage probability and Shannon rate at these epochs. We can make an analogy with ``seasons'' based on the fluctuations of signal and interference power. Strong or mild signal or interference power correspond to different seasons of Shannon rate along the evolution of the system. We also provide a complete comparison study of the metrics at interest at these epochs.

math.PR↗

arXiv2026

Shortest Path Lengths in Poisson Line Cox Processes: Approximations and Applications

We study street-constrained ($\ell_1$) shortest paths in a Poisson line Cox process (PLCP), where Poisson points of linear intensity $μ$ lie on the lines of an underlying Poisson line process (PLP) of density $λ$. Under a one-turn restriction, we derive closed-form expressions for the distribution of the nearest-neighbor path length from (i) the typical PLCP point and (ii) the typical PLP intersection, by explicitly evaluating the relevant void probabilities via a geometric decomposition of the feasible path-length set. For the intersection case, we further provide analytically tractable upper and lower bounds that capture the impact of $λ$ and $μ$. Allowing two turns from the typical point, we obtain a computable upper bound using a feasible-set shrinking argument and identify regimes in which it is tight. We also delineate parameter ranges where a one-turn route from a typical intersection can outperform a two-turn route from a typical point. Finally, we discuss how the results enable statistical performance characterization of ride-hailing services in terms of service guarantee, trip time, and consequently, derive dimensioning insights. We also illustrate qualitatively, how the results can be employed to study vehicle-to-vehicle communication broadcast messages near intersections.

cs.IT↗

arXiv2026

Large and moderate deviations in Poisson navigations

We derive large- and moderate-deviation results in random networks given as planar directed navigations on homogeneous Poisson point processes. In this non-Markovian routing scheme, starting from the origin, at each consecutive step a Poisson point is joined by an edge to its nearest Poisson point to the right within a cone. We establish precise exponential rates of decay for the probability that the vertical displacement of the random path is unexpectedly large. The proofs rest on controlling the dependencies of the individual steps and the randomness in the horizontal displacement as well as renewal-process arguments.

math.PR↗

arXiv2023

Poisson approximation of fixed-degree nodes in weighted random connection models

We present a process-level Poisson-approximation result for the degree-k vertices in a high-density weighted random connection model with preferential-attachment kernel in the unit volume. Our main focus lies on the impact of the left tails of the weight distribution for which we establish general criteria based on their small-weight quantiles. To illustrate that our conditions are broadly applicable, we verify them for weight distributions with polynomial and stretched exponential left tails. The proofs rest on truncation arguments and a recently established quantitative Poisson approximation result for functionals of Poisson point processes.

math.PR↗

arXiv2023

Continuum Percolation in a Nonstabilizing Environment

We prove phase transitions for continuum percolation in a Boolean model based on a Cox point process with nonstabilizing directing measure. The directing measure, which can be seen as a stationary random environment for the classical Poisson--Boolean model, is given by a planar rectangular Poisson line process. This Manhattan grid type construction features long-range dependencies in the environment, leading to absence of a sharp phase transition for the associated Cox--Boolean model. The phase transitions are established under individually as well as jointly varying parameters. Our proofs rest on discretization arguments and a comparison to percolation on randomly stretched lattices established in Hoffman 2005.

math.PR↗