Generalized Random Sequential Adsorption on Erdős–Rényi Random Graphs

Dhara, Souvik; Leeuwaarden, Jsh Johan van; Mukherjee, Debankur

doi:10.1007/s10955-016-1583-z

Cited by 10 publications

(13 citation statements)

References 24 publications

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“…Denote this unique value by α d , to express its dependence on the dimension d. In Section 6, we show that In contrast to the Euclidean space, rsa on the crg(c, α d ) model is analytically solvable, even at later times when the filled space becomes more dense (large c). To do so, we will extend the mean-field techniques recently developed for analyzing rsa on random graph models [4,6,13,32]. The main goal of these works was to find greedy independent sets (or colorings) of large random networks.…”

Section: Clustered Random Graphsmentioning

confidence: 99%

“…In particular, we will prove Theorem 3.1. We first introduce an algorithm that sequentially activates the vertices while obeying the hard-core exclusion constraint, and then analyze the exploration algorithm (see [5,6,13] for similar analyses in various other contexts). The idea is to keep track of the number of vertices that are not neighbors of already actives vertices (termed unexplored vertices), so that when this number becomes zero, no vertex can be activated further.…”

Section: Proof Of Theorem 31mentioning

confidence: 99%

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Corrected Mean-Field Model for Random Sequential Adsorption on Random Geometric Graphs

2018

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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 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 blocking on a sequence of clustered random graphs. This random network model can be thought of as a corrected mean-field model for the interaction graph between the attempted spheres. Using functional limit theorems, we characterize the fraction of accepted spheres and its fluctuations.

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Section: Clustered Random Graphsmentioning

confidence: 99%

Section: Proof Of Theorem 31mentioning

confidence: 99%

Corrected Mean-Field Model for Random Sequential Adsorption on Random Geometric Graphs

2018

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“…graphs with few loops, can be also tractable. For instance, the RSA model on the sparse Erdős-Rényi random graphs with b = 1 has been studied, see [39][40][41][42]. It would be interesting to determine the full counting statistics of the occupation number for this RSA model.…”

Section: Discussionmentioning

confidence: 99%

Large Deviations in One-Dimensional Random Sequential Adsorption

Krapivsky

2020

Preprint

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In a random sequential adsorption process, objects are deposited randomly, irreversibly, and sequentially; if an attempt to add an object results in an overlap with previously deposited objects, the attempt is discarded. The process continues until the system reaches a jammed state when no further additions are possible. Exact analyses have been performed only in one-dimensional models, and the average number of absorbed particles has been computed in a few solvable situations. We analyze a process in which landing on an empty site is allowed when at least b neighboring sites on the left and the right are empty. For the minimal model (b = 1), we compute the full counting statistics of the occupation number.

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“…Theorems 1-3 also contribute to the mathematical perspective. The study of exploration processes of the RSA type on random graphs has seen interest in recent years [20,[32][33][34][35][36][37][38]. The tools necessary from probability theory to analyze said processes include e.g.…”

Section: Introductionmentioning

confidence: 99%

Modeling Rydberg Gases using Random Sequential Adsorption on Random Graphs

Rutten,

Sanders

2020

Preprint

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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 particular subgraph of a mixture of two other random graphs. Contrary to the former two models, it lends itself for a rigorous mathematical analysis; and it is built specifically to have particular structural properties of a RGG. We establish for it a fluid limit describing the time-evolution of number of Rydberg atoms, and show numerically that the expression remains accurate across a wider range of particle densities than an earlier approach based on an RSA process on an Erdös-Rényi Random Graph (ERRG). Finally, we also come up with a new heuristic using random graphs that gives a recursion to describe a normalized pair-correlation function of a Rydberg gas. Our results suggest that even without dissipation, on long time scales the statistics are affected most by the geometrical restrictions induced by blockade effects, while on short time scales the statistics are affected most by quantum mechanical effects.

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Generalized Random Sequential Adsorption on Erdős–Rényi Random Graphs

Cited by 10 publications

References 24 publications

Corrected Mean-Field Model for Random Sequential Adsorption on Random Geometric Graphs

Corrected Mean-Field Model for Random Sequential Adsorption on Random Geometric Graphs

Large Deviations in One-Dimensional Random Sequential Adsorption

Modeling Rydberg Gases using Random Sequential Adsorption on Random Graphs

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