随机顺序吸附的预期持续时间

Asymptotic normality of maximum likelihood estimator for cooperative sequential adsorption

We have shown in previous work that statistical inference for cooperative sequential adsorption model can be based on maximum likelihood estimation. In this paper we continue this research and establish asymptotic normality of the maximum likelihood estimator in thermodynamic limit. We also perform and discuss some numerical simulations of the model.

由合作序贯吸附启发的概率模型

Probabilistic models motivated by cooperative sequential adsorption

本文综述了由合作序贯吸附模型启发的概率模型，涵盖其在欧氏空间和图上的随机序贯分配表述，以及相应的空间或整数值生灭过程。

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…

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…