Related papers: Random presentations and random subgroups: a surve…
We present an accessible introduction to basic results on groups of intermediate growth.
This paper deals with (finite or infinite) sequences of arbitrary independent events in some probability space. We find sharp lower bounds for the probability of a union of such events when the sum of their probabilities is given. The…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
A qualitative (and selective) discussion of current activities and problems in the field is given.
Randomness is a crucial resource for a broad range of important applications, such as Monte Carlo simulation and computation, generative artificial intelligence and cryptography. But what is randomness? A widely accepted definition has…
Pedestrians are often encountered walking in the company of some social relations, rather than alone. The social groups thus formed, in variable proportions depending on the context, are not randomly organised but exhibit distinct features,…
This is neither a summary talk (too much for too short a talk) nor a conclusion (a gigantic work is in progress and we are not at the end of a particular phase), rather an overview of the field as reflected at this Conference.
This is a research monograph on constructions of and group actions on countable homogeneous graphs, concentrating particularly on the simple random graph and its edge-coloured variants. We study various aspects of the graphs, but the…
Ad hoc teamwork is the research problem of designing agents that can collaborate with new teammates without prior coordination. This survey makes a two-fold contribution: First, it provides a structured description of the different facets…
We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
I present a brief survey of surveys, and their results and implications, intended to set the context for the ensuing discussion.
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
Analyzing open-ended survey responses is a crucial yet challenging task for social scientists, non-profit organizations, and educational institutions, as they often face the trade-off between obtaining rich data and the burden of reading…
This note contains old instead of new results about random walks on groups, which may serve as a small supplement to the author's monograph ``Random Walks on Infinite Graphs and Groups'' (Cambridge Univ. Press 2000/2009). First, we exhibit…
We consider random graphs sampled uniformly from a structured class of graphs, such as the class of graphs embeddable in a given surface. We sharpen and extend earlier results on pendant appearances, concerning for example numbers of…
The first three sections of this survey represent an updated and much expanded version of the abstract of my talk at FPSAC'2010: new results are incorporated and several concrete conjectures on the interactions between the three…
A class of groups is investigated, each of which has a fairly simple presentation . For example the group $R = (a, b, c, d | a^3 = b^3 = c^3 = d^3 = 1, ba^{-1} =dc^{-1}, ca^{-1} = db^{-1}) $ is in the class. Such a group does not have as a…
This expository article revolves around the question to find short presentations of finite simple groups. This subject is one of the most active research areas of group theory in recent times. We bring together several known results on…