Mathew D. Penrose, Tom Rosoman
Consider random sequential adsorption on a red/blue chequerboard lattice with arrivals at rate $1$ on the red squares and rate $λ$ on the blue squares. We prove that the critical value of $λ$, above which we get an infinite blue component, is finite and strictly greater than $1$.
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Consider random sequential adsorption on a chequerboard lattice with arrivals at rate $1$ on light squares and at rate $λ$ on dark squares. Ultimately, each square is either occupied, or blocked by an occupied neighbour. Colour the occupied dark squares and blocked light sites {\em black}, and the remaining squares {\em white}. Independently at each meeting-point of four squares, allow diagonal connections between black squares with probability $p$; otherwise allow diagonal connections between white squares. We show that there is a critical surface of pairs $(λ, p)$, containing the pair $(1,0.…
Multidisperse Random Sequential Adsorption and Generalizations
本文统一研究了一维随机顺序吸附（RSA）过程中线段长度取自给定分布时的极限密度，给出了通用界限并刻画了多分散RSA和幂律RSA等具体情形。
We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity of the model is that the probability distribution of a point depends on previously allocated points. We assume that the dependence vanishes as the concentration of points tends to infinity. Under this assumption the law of large numbers, the central limit theorem and Poisson approximation are proved for the generated sequence of random point measures.
When gas molecules bind to a surface they may do so in such a way that the adsorption of one molecule inhibits the arrival of others. We consider random sequential adsorption in which the empty sites of a graph are irreversibly occupied in random order by a variety of types of ``particles.'' In a finite region the process terminates when no more particles can arrive. A universal asymptotic formula for the mean duration is given.
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…
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。
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.
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。
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…
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…
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.
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…
The critical percolation window in growing random graphs
研究了生长随机图中临界渗流窗口的性质，揭示了窗口宽度、最大组件大小及易感性特征。
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。
In this article, we study a type of a one dimensional percolation model whose basic features include a sequential dropping of particles on a substrate followed by their transport via a pushing mechanism (see [S. N. Majumdar and D. S. Dean, Phys. Rev. Ltt. A 11, 89 (2002)]). Consider an empty one dimensional lattice with n empty sites and periodic boundary conditions (as a necklace with n rings). Imagine then the particles which drop sequentially on this lattice, uniformly at random on one of the n sites. Letting a site can settles at most one particle, if a particle drops on an empty site, it …
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