Related papers: Order-invariant measures on fixed causal sets
We consider positively supported Borel measures for which all moments exist. On the set of compactly supported measures in this class a partial order is defined via eventual dominance of the moment sequences. Special classes are identified…
The general notion of a stochastic ordering is that one probability distribution is smaller than a second one if the second attaches more probability to higher values than the first. Motivated by recent work on barycentric maps on spaces of…
Prior work has shown that causal structure can be uniquely identified from observational data when these follow a structural equation model whose error terms have equal variances. We show that this fact is implied by an ordering among…
In quantum mechanics events can happen in no definite causal order: in practice this can be verified by measuring a causal witness, in the same way that an entanglement witness verifies entanglement. Indefinite causal order can be observed…
We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence…
Adjusting for covariates is a well established method to estimate the total causal effect of an exposure variable on an outcome of interest. Depending on the causal structure of the mechanism under study there may be different adjustment…
In the causal set approach to discrete quantum gravity the universe grows one element at a time in discrete steps. At each step the process has the form of a causal set (causet) and the "completed" universe is given by a path through a…
How should researchers analyze randomized experiments in which the main outcome is latent and measured in multiple ways but each measure contains some degree of error? We first identify a critical study-specific noncomparability problem in…
Correlation measure of order $k$ is an important measure of randomness in binary sequences. This measure tries to look for dependence between several shifted version of a sequence. We study the relation between the correlation measure of…
We investigate extension of a measure to a very general set of undetermined structure. Structure may be imposed on this set in special cases
Multiple metrics have been developed to detect causality relations between data describing the elements constituting complex systems, all of them considering their evolution through time. Here we propose a metric able to detect causality…
Causal spaces have recently been introduced as a measure-theoretic framework to encode the notion of causality. While it has some advantages over established frameworks, such as structural causal models, the theory is so far only developed…
Quantum causality extends the conventional notion of fixed causal structure by allowing channels and operations to act in an indefinite causal order. The importance of such an indefinite causal order ranges from the foundational---e.g.…
We study poset limits given by sequences of finite interval orders or, as a special case, finite semiorders. In the interval order case, we show that every such limit can be represented by a probability measure on the space of closed…
We consider the problem of computing the measure of a regular set of infinite binary trees. While the general case remains unsolved, we show that the measure of a language can be computed when the set is given in one of the following three…
Let $U_0,U_1$ be two normal measures on $\kappa .$ We say that $U_0$ is in the Mitchell ordering less then $U_1,$ $U_0\vartriangleleft U_1,$ if $U_0 \in Ult(V,U_1) .$ The ordering is well-known to be transitive and well-founded. It has been…
The quantum switch, the canonical example of a process with indefinite causal order, has been claimed to provide various advantages over processes with definite causal orders for some particular tasks in the field of quantum metrology. In…
Sequential measurements of non-commuting observables produce order effects that are well-known in quantum physics. But their conceptual basis, a significant measurement interaction, is relevant for far more general situations. We argue that…
We consider the limit set of generalised iterated function systems. Under the assumption of a natural potential, the so called cylinder function, we prove the existence of the invariant probability measure satisfying the equilibrium state.…
The causal set approach to quantum gravity is based on the hypothesis that the underlying structure of spacetime is that of a random partial order. We survey some of the interesting mathematics that has arisen in connection with the causal…