Limit theorems for random point measures generated by cooperative sequential adsorption

Generalized random sequential adsorption on Erdős-Rényi random graphs

We investigate Random Sequential Adsorption (RSA) on a random graph via the following greedy algorithm: Order the $n$ vertices at random, and sequentially declare each vertex either active or frozen, depending on some local rule in terms of the state of the neighboring vertices. The classical RSA rule declares a vertex active if none of its neighbors is, in which case the set of active nodes forms an independent set of the graph. We generalize this nearest-neighbor blocking rule in three ways and apply it to the Erdős-Rényi random graph. We consider these generalizations in the large-graph lim…

随机序列吸附模型中的密度与相关性

Density and correlation in a random sequential adsorption model

本文研究了一维格点上带最近邻排斥的随机序列吸附过程，提出了一种计算占据位置密度和对相关函数的方法。

Large Deviations in One-Dimensional Random Sequential Adsorption

In random sequential adsorption (RSA), objects are deposited randomly, irreversibly, and sequentially; attempts leading to an overlap with previously deposited objects are discarded. The process continues until the system reaches a jammed state when no further additions are possible. We analyze a class of lattice RSA models in which landing on an empty site in a segment is allowed when at least $b$ neighboring sites on the left and the right are unoccupied. For the minimal model ($b=1$), we compute the full counting statistics of the occupation number. We reduce the determination of the full c…

Stability of a growth process generated by monomer filling with nearest-neighbour cooperative effects

We study stability of a growth process generated by sequential adsorption of particles on a one-dimensional lattice torus, that is, the process formed by the numbers of adsorbed particles at lattice sites, called heights. Here the stability of process, loosely speaking, means that its components grow at approximately the same rate. To assess stability quantitatively, we investigate the stochastic process formed by differences of heights. The model can be regarded as a variant of a Polya urn scheme with local geometric interaction.

Corrected mean-field model for random sequential adsorption on random geometric graphs

A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the $d$-dimensional Euclidean space with $d\geq 2$. Spheres arrive sequentially at uniformly chosen locations in space and are accepted only when there is no overlap with previously deposited spheres. Due to spatial correlations, characterizing the fraction of accepted spheres remains largely intractable. We study this fraction by taking a novel approach that compares random sequential adsorption in Euclidean space to the nearest-neighbor blockin…

Localisation in a growth model with interaction

This paper concerns the long term behaviour of a growth model describing a random sequential allocation of particles on a finite cycle graph. The model can be regarded as a reinforced urn model with graph-based interactions. It is motivated by cooperative sequential adsorption, where adsorption rates at a site depend on the configuration of existing particles in the neighbourhood of that site. Our main result is that, with probability one, the growth process will eventually localise either at a single site, or at a pair of neighbouring sites.

Modeling Rydberg Gases using Random Sequential Adsorption on Random Graphs

The statistics of strongly interacting, ultracold Rydberg gases are governed by the interplay of two factors: geometrical restrictions induced by blockade effects, and quantum mechanical effects. To shed light on their relative roles in the statistics of Rydberg gases, we compare three models in this paper: a quantum mechanical model describing the excitation dynamics within a Rydberg gas, a Random Sequential Adsorption (RSA) process on a Random Geometric Graph (RGG), and a RSA process on a Decomposed Random Intersection Graph (DRIG). The latter model is new, and refers to choosing a particula…

一维随机序列吸附及其连续极限若干方面的新视角

A new look at some aspects of one-dimensional random sequential adsorption and its continuum limit

本文研究一维随机序列吸附（RSA）的离散键合模型，分析键合间隙的渐近分布及多尺度键合的渐近行为，拓展了Rényi停车常数相关的理论结果。

LISA: Locally Interacting Sequential Adsorbtion

We study a class of dynamically constructed point processes in which at every step a new point (particle) is added to the current configuration with a distribution depending on the local structure around a uniformly chosen particle. This class covers, in particular, generalised Polya urn scheme, Dubbins--Freedman random measures and cooperative sequential adsorption models studied previously. Specifically, we address models where the distribution of a newly added particle is determined by the distance to the closest particle from the chosen one. We address boundedness of the processes and conv…