Related papers: Truncation in Duality and Intertwining Kernels
We present a theorem which elucidates the connection between self-duality of Markov processes and representation theory of Lie algebras. In particular, we identify sufficient conditions such that the intertwining function between two…
We develop a general theory of intertwined diffusion processes of any dimension. Our main result gives an SDE construction of intertwinings of diffusion processes and shows that they correspond to nonnegative solutions of hyperbolic partial…
String-theoretic T-duality can be exploited to simplify some features of the bulk-boundary correspondence in condensed matter theory. This paper surveys how T-duality links position and momentum space pictures of that correspondence.
We use reproducing kernel methods to study various rigidity problems. The methods and setting allow us to also consider the non-positive case.
Monotonicity and recursivity are central assumptions in intertemporal consumption problems under ambiguity. We show that monotone recursive preferences admit both a recursive and an ex-ante representation, and that the certainty equivalent…
We study the intermittency properties of two branching processes, one with a uniform and another with a singular splitting kernel. The asymptotic intermittency indices, as well as the leading corrections to the asymptotic linear regime are…
Machine learning of scalar molecular properties such as potential energy has enabled widespread applications. However, there are relatively few machine learning models targeting directional properties, including permanent and transition…
We develop a framework to track the structure of temporal networks with a signal processing approach. The method is based on the duality between networks and signals using a multidimensional scaling technique. This enables a study of the…
We investigate the intertwining of Laguerre processes of parameter $\alpha$ in different dimensions. We introduce a Feller kernel that depends on $\alpha $ and intertwines the $\alpha$-Laguerre process in $N+1$ dimensions and that in $N$…
In these lecture notes we present some connections between random matrices, the asymmetric exclusion process, random tilings. These three apparently unrelated objects have (sometimes) a similar mathematical structure, an interlacing…
We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure $\mu$ has zeros in some prescribed entries. We describe precisely which pattern of these zeroes corresponds to independence, namely, the…
In the context of earlier work, we investigate the emergence of a "distance" in the physical world. For this we consider a Cantor ternary like process, but much more general: properties like perfectness and disconnectedness are not invoked,…
In truncated partial-wave analysis, one fits observables that are bilinear in the amplitudes rather than the amplitudes themselves. Truncation is therefore not merely a restriction of the amplitude basis, but of the bilinear interference…
Previously, we demonstrated that the dynamics of kicked spin chains possess a remarkable duality property. The trace of the unitary evolution operator for $N$ spins at time $T$ is related to one of a non-unitary evolution operator for $T$…
We present a strong-weak coupling duality for quantum mechanical potentials. Similarly to what happens in quantum field theory, it relates two problems with inverse couplings, leading to a mapping of the strong coupling regime into the weak…
We establish a direct link between the time-reversal technique and the so-called adjoint method for imaging. Using this relationship, we derive new solution strategies for an inverse problem which arises in telecommunication. These…
Well-known Nuclear Magnetic Resonance experiments show that the time evolution according to (truncated) dipole-dipole interactions between n spins can be inverted by simple pulse sequences. Independent of n, the reversed evolution is only…
In this paper we review some results on time-homogeneous birth-death processes. Specifically, for truncated birth-death processes with two absorbing or two reflecting endpoints, we recall the necessary and sufficient conditions on the…
The explicit integrability of second order ordinary differential equations invariant under time-translation and rescaling is investigated. Quadratic systems generated from the linearisable version of this class of equations are analysed to…
We extend the duality between massive and topologically massive antisymmetric tensor gauge theories in arbitrary space-time dimensions to include topological defects. We show explicitly that the condensation of these defects leads, in 4…