Related papers: Poset limits and exchangeable random posets

Tests for proportional hazards assumption concerning specified covariates or groups of covariates are proposed. The class of alternatives is wide: log-hazard rates under different values of covariates may cross, approach, go away. The data…

In this paper we study the boundedness of extension operators associated with spheres in vector spaces over finite fields.In even dimensions, we estimate the number of incidences between spheres and points in the translated set from a…

De Finetti's classical result of [18] identifying the law of an exchangeable family of random variables as a mixture of i.i.d. laws was extended to structure theorems for more complex notions of exchangeability by Aldous [1,2,3], Hoover…

We present a construction of the Steinberg representation admitting an automatic pass to an infinite-dimensional limit.

We study some percolation problems on the complete graph over $\mathbf N$. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the…

We consider probability measure preserving discrete groupoids, group actions and equivalence relations in the context of general probability spaces. We study for these objects the notions of cost, $\beta$-invariant and some…

We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…

We introduce two novel ideas related to the crosscut poset and give many examples of application of these ideas to the fixed point property.

We consider an infinite balls-in-boxes occupancy scheme with boxes organised in nested hierarchy, and random probabilities of boxes defined in terms of iterated fragmentation of a unit mass. We obtain a multivariate functional limit theorem…

We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of…

This paper reformulates a classical result in probability theory from the 1930s in modern categorical terms: de Finetti's representation theorem is redescribed as limit statement for a chain of finite spaces in the Kleisli category of the…

In this note, we give a probabilistic interpretation of the Central Limit Theorem used for approximating isotropic Gaussians in [1].

We present new mixture representations for the generalized Linnik distribution in terms of normal, Laplace, exponential and stable laws and establish the relationship between the mixing distributions in these representations. Based on these…

We develop a new method to compute the homology groups of finite topological spaces (or equivalently of finite partially ordered sets) by means of spectral sequences giving a complete and simple description of the corresponding…

We consider various regular graphs defined on the set of elements of given rank of a finite polar space. It is likely that no two such graphs, of the same kind but defined for different ranks, can have the same degree. We shall prove this…

We introduce and study VERSs (vertex and edge replacement systems) as a technology of graph expansions. We consider its history graph, an augmented tree that records each graph expansion, and we provide sufficient conditions under which it…

We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…

We introduce persistence with an emphasis on its algebraic foundations, using the representation theory of posets. Linear representations of posets arise in several areas of mathematics, including the representation theory of quivers and…

We propose a simple algorithm generating labelled posets of given size according to the almost uniform distribution. By "almost uniform" we understand that the distribution of generated posets converges in total variation to the uniform…

This paper studies majorization of high tensor powers of finitely supported probability distributions. Viewing probability distributions as a resource with majorization as a means of transformation corresponds to the resource theory of pure…