Related papers: Riemann surfaces for integer counting processes
Using vertex algebra techniques, we determine a set of generators for the cohomology ring of the Hilbert schemes of points on an arbitrary smooth projective surface over the field of complex numbers.
We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…
We define refined invariants which "count" nodal curves in sufficiently ample linear systems on surfaces, conjecture that their generating function is multiplicative, and conjecture explicit formulas in the case of K3 and abelian surfaces.…
We find sufficient conditions for a discrete sequence to be interpolating or sampling for certain generalized Bergman spaces on open Riemann surfaces. As in previous work of Bendtsson, Ortega-Cerda, Seip, Wallsten and others, our conditions…
We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar surfaces. Central to this work is the comparison of two…
Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…
The treatment of the number-theoretical problem of integer partitions within the approach of statistical mechanics is discussed. Historical overview is given and known asymptotic results for linear and plane partitions are reproduced. From…
A method is presented in which matrix elements for some processes are calculated recursively. This recursive calculational technique is based on the method of basis spinors.
In this paper, we address the following question: What does a typical compact Riemann surface of large genus look like geometrically? We do so by constructing compact Riemann surfaces from oriented 3-regular graphs. The set for such Riemann…
These lecture notes present a computation driven pathway from classical complex analysis to the theory of compact Riemann surfaces and their connections to algebraic geometry. The exposition follows a compute first then abstract philosophy,…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We study rate of convergence of recursive estimation procedures for the general…
Let S be a surface obtained from a plane polygon by identifying infinitely many pairs of segments along its boundary. A condition is given under which the complex structure in the interior of the polygon extends uniquely across the quotient…
Using the methods developed in [LQW], math.AG/0009132, we obtain a second set of generators for the cohomology ring of the Hilbert scheme of points on an arbitrary smooth projective surface over the field of complex numbers. These…
A research frontier has emerged in scientific computation, wherein numerical error is regarded as a source of epistemic uncertainty that can be modelled. This raises several statistical challenges, including the design of statistical…
A new parametric integral is obtained as a consequence of the Riemann hypothesis. An asymptotic multiplicability is the main property of this integral.
Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…
We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential…
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. In this…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
An existing dialogue between number theory and dynamical systems is advanced. A combinatorial device gives necessary and sufficient conditions for a sequence of non-negative integers to count the periodic points in a dynamical system. This…