Multiple change-points with an application to financial modeling.

Orasch, Markus

doi:10.22215/etd/1999-04196

Cited by 2 publications

(3 citation statements)

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“…At larger values of µ we see the emergence of topologically stabilized configurations which are hard to update and lead to very long autocorrelations. For the particularly challenging two-dimensional case the recently proposed canonical worldline approach [22] could be a powerful alternative which we currently explore.…”

Section: Results For the Two-flavor Modelmentioning

confidence: 99%

Dual simulation of the massless lattice Schwinger model with topological term and non-zero chemical potential

Göschl

2018

EPJ Web Conf.

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We discuss simulation strategies for the massless lattice Schwinger model with a topological term and finite chemical potential. The simulation is done in a dual representation where the complex action problem is solved and the partition function is a sum over fermion loops, fermion dimers and plaquette-occupation numbers. We explore strategies to update the fermion loops coupled to the gauge degrees of freedom and check our results with conventional simulations (without topological term and at zero chemical potential), as well as with exact summation on small volumes. Some physical implications of the results are discussed.

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Section: Results For the Two-flavor Modelmentioning

confidence: 99%

Dual simulation of the massless lattice Schwinger model with topological term and non-zero chemical potential

Göschl

2018

EPJ Web Conf.

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“…The coupling of matter fields proceeds in the same way as we discussed for SU (2). We again use the staggered discretization of the fermion action (21), and the dualization of the fermion partition sum reads as in (22), with the only difference that for SU(3) the color labels run from 1 to 3. The power of the overall factor in front of the sum over the configurations of the fermion dual variables {s, k, k} here is 3V instead of 2V.…”

Section: Dual Representation Of Full Lattice Qcdmentioning

confidence: 99%

“…The geometrical interpretation of the net-particle numbers as temporal winding numbers implies that for each individual configuration of the dual variables we can determine the net-particle numbers as integers -a property which is not shared by the conventional representation where the net particle number corresponds to a lattice discretization of the continuum Noether charge, which is not necessarily integer. Thus, in the worldline representation it is straightforward to set up a canonical simulation, i.e., a simulation at fixed net-particle number (compare [21]).…”

Section: Introductionmentioning

confidence: 99%

Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

2018

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We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.Speaker, can be integrated out in closed form. In particular for non-abelian gauge theories the lack of a suitable reordering strategy quickly leads to a proliferation of rather non-local couplings in the resulting dual representation. However, for several (spin-) systems with non-abelian symmetries successful complete dualizations 1 were discussed recently [1,[6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In all cases a suitable representation was found such that after strong coupling expansion of local Boltzmann factors the original degrees of freedom could be integrated out in closed form. This is a strategy that led to interesting worldline representations for several non-abelian systems and is also the basis for the approach reviewed here.In our contribution we discuss results for a recently introduced strategy for the dualization of nonabelian theories. In the so-called Abelian color flux and Abelian color cycle approaches one writes all traces and matrix/vector products as sums over color indices (or more generally over 'internal indices') and introduces a dual variable for each individual contribution. At this stage of the dualization the dual variables are simply the expansion indices used for the Taylor series of the individual Boltzmann factors. All terms in the corresponding expansion are complex n...

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Multiple change-points with an application to financial modeling.

Cited by 2 publications

References 0 publications

Dual simulation of the massless lattice Schwinger model with topological term and non-zero chemical potential

Dual simulation of the massless lattice Schwinger model with topological term and non-zero chemical potential

Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

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