TY  - JOUR
A1  - Boldrighini, Carlo
A1  - Frigio, Sandro
A1  - Maponi, Pierluigi
A1  - Pellegrinotti, Alessandro
A1  - Sinai, Yakov G.
T1  - 3-D incompressible Navier-Stokes equations: Complex blow-up and related real flows
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472201
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 185
EP  - 194
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Figari, Rodolfo
A1  - Teta, Alessandro
T1  - Zero-range hamiltonians for three quantum particles
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472189
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 175
EP  - 184
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Houdebert, Pierre
T1  - Numerical study for the phase transition of the area-interaction model
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472177
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 165
EP  - 174
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Jansen, Sabine
A1  - Kuna, Tobias
A1  - Tsagkarogiannis, Dimitrios
T1  - Virial inversion for inhomogeneous systems
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472111
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 135
EP  - 144
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Hryniv, Ostap
A1  - Wallace, Clare
T1  - Phase separation and sharp large deviations
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472168
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 155
EP  - 164
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Jansen, Sabine
A1  - Kolesnikov, Leonid
T1  - Activity expansions for Gibbs correlation functions
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472121
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 145
EP  - 154
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Jansen, Sabine
A1  - Tsagkarogiannis, Dimitrios
T1  - Mayer expansion for the Asakura-Oosawa model of colloid theory
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472109
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 127
EP  - 134
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Piatnitski, Andrey
A1  - Zhizhina, Elena
T1  - Non-local convolution type parabolic equations with fractional and regular time derivative
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472024
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 65
EP  - 67
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Jursenas, Rytis
T1  - The peak model for finite rank supersingular perturbations
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472090
IS  - 6
SP  - 117
EP  - 126
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Mazzonetto, Sara
T1  - On an approximation of 2-D stochastic Navier-Stokes equations
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472053
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 87
EP  - 96
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Pechersky, Eugeny
A1  - Pirogov, Sergei
A1  - Yambartsev, Anatoly
T1  - Large emissions
BT  - Hawking-Penrose black hole model
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472049
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 77
EP  - 86
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Poghosyan, Suren
A1  - Zessin, Hans
T1  - Construction of limiting Gibbs processes and the uniqueness of Gibbs processes
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472015
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 55
EP  - 64
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Lykov, Alexander
A1  - Malyshev, Vadim
T1  - When bounded chaos becomes unbounded
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472060
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 97
EP  - 106
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Khachatryan, Linda
A1  - Nahapetian, Boris
T1  - On direct and inverse problems in the description of lattice random fields
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472083
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 107
EP  - 116
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Rafler, Mathias
T1  - Pinned Gibbs processes
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472007
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 45
EP  - 53
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Rœlly, Sylvie
A1  - Zass, Alexander
T1  - Marked Gibbs point processes with unbounded interaction
BT  - An existence result
JF  - Journal of statistical physics
N2  - We construct marked Gibbs point processes in R-d under quite general assumptions. Firstly, we allow for interaction functionals that may be unbounded and whose range is not assumed to be uniformly bounded. Indeed, our typical interaction admits an a.s. finite but random range. Secondly, the random marks-attached to the locations in R-d-belong to a general normed space G. They are not bounded, but their law should admit a super-exponential moment. The approach used here relies on the so-called entropy method and large-deviation tools in order to prove tightness of a family of finite-volume Gibbs point processes. An application to infinite-dimensional interacting diffusions is also presented.
KW  - Marked Gibbs process
KW  - Infinite-dimensional interacting diffusion
KW  - Specific entropy
KW  - DLR equation
Y1  - 2020
U6  - https://doi.org/10.1007/s10955-020-02559-3
SN  - 0022-4715
SN  - 1572-9613
VL  - 179
IS  - 4
SP  - 972
EP  - 996
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Sanchez, Sabrina
A1  - Wicht, Johannes
A1  - Bärenzung, Julien
T1  - Predictions of the geomagnetic secular variation based on the ensemble sequential assimilation of geomagnetic field models by dynamo simulations
JF  - Earth, planets and space
N2  - The IGRF offers an important incentive for testing algorithms predicting the Earth's magnetic field changes, known as secular variation (SV), in a 5-year range. Here, we present a SV candidate model for the 13th IGRF that stems from a sequential ensemble data assimilation approach (EnKF). The ensemble consists of a number of parallel-running 3D-dynamo simulations. The assimilated data are geomagnetic field snapshots covering the years 1840 to 2000 from the COV-OBS.x1 model and for 2001 to 2020 from the Kalmag model. A spectral covariance localization method, considering the couplings between spherical harmonics of the same equatorial symmetry and same azimuthal wave number, allows decreasing the ensemble size to about a 100 while maintaining the stability of the assimilation. The quality of 5-year predictions is tested for the past two decades. These tests show that the assimilation scheme is able to reconstruct the overall SV evolution. They also suggest that a better 5-year forecast is obtained keeping the SV constant compared to the dynamically evolving SV. However, the quality of the dynamical forecast steadily improves over the full assimilation window (180 years). We therefore propose the instantaneous SV estimate for 2020 from our assimilation as a candidate model for the IGRF-13. The ensemble approach provides uncertainty estimates, which closely match the residual differences with respect to the IGRF-13. Longer term predictions for the evolution of the main magnetic field features over a 50-year range are also presented. We observe the further decrease of the axial dipole at a mean rate of 8 nT/year as well as a deepening and broadening of the South Atlantic Anomaly. The magnetic dip poles are seen to approach an eccentric dipole configuration.
KW  - Earth's magnetic field
KW  - Geomagnetic secular variation
KW  - Dynamo
KW  - simulations
KW  - Data assimilation
Y1  - 2020
U6  - https://doi.org/10.1186/s40623-020-01279-y
SN  - 1880-5981
VL  - 72
IS  - 1
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Garbuno-Inigo, Alfredo
A1  - Nüsken, Nikolas
A1  - Reich, Sebastian
T1  - Affine invariant interacting Langevin dynamics for Bayesian inference
JF  - SIAM journal on applied dynamical systems
N2  - We propose a computational method (with acronym ALDI) for sampling from a given target distribution based on first-order (overdamped) Langevin dynamics which satisfies the property of affine invariance. The central idea of ALDI is to run an ensemble of particles with their empirical covariance serving as a preconditioner for their underlying Langevin dynamics. ALDI does not require taking the inverse or square root of the empirical covariance matrix, which enables application to high-dimensional sampling problems. The theoretical properties of ALDI are studied in terms of nondegeneracy and ergodicity. Furthermore, we study its connections to diffusion on Riemannian manifolds and Wasserstein gradient flows. Bayesian inference serves as a main application area for ALDI. In case of a forward problem with additive Gaussian measurement errors, ALDI allows for a gradient-free approximation in the spirit of the ensemble Kalman filter. A computational comparison between gradient-free and gradient-based ALDI is provided for a PDE constrained Bayesian inverse problem.
KW  - Langevin dynamics
KW  - interacting particle systems
KW  - Bayesian inference
KW  - gradient flow
KW  - multiplicative noise
KW  - affine invariance
KW  - gradient-free
Y1  - 2020
U6  - https://doi.org/10.1137/19M1304891
SN  - 1536-0040
VL  - 19
IS  - 3
SP  - 1633
EP  - 1658
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Froyland, Gary
A1  - Koltai, Peter
A1  - Stahn, Martin
T1  - Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration
JF  - SIAM journal on applied dynamical systems
N2  - Understanding the macroscopic behavior of dynamical systems is an important tool to unravel transport mechanisms in complex flows. A decomposition of the state space into coherent sets is a popular way to reveal this essential macroscopic evolution. To compute coherent sets from an aperiodic time-dependent dynamical system we consider the relevant transfer operators and their infinitesimal generators on an augmented space-time manifold. This space-time generator approach avoids trajectory integration and creates a convenient linearization of the aperiodic evolution. This linearization can be further exploited to create a simple and effective spectral optimization methodology for diminishing or enhancing coherence. We obtain explicit solutions for these optimization problems using Lagrange multipliers and illustrate this technique by increasing and decreasing mixing of spatial regions through small velocity field perturbations.
KW  - coherent set
KW  - mixing
KW  - transfer operator
KW  - infinitesimal generator
KW  - unsteady flow
KW  - mixing optimization
Y1  - 2020
U6  - https://doi.org/10.1137/19M1261791
SN  - 1536-0040
VL  - 19
IS  - 3
SP  - 1659
EP  - 1700
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Rastogi, Abhishake
T1  - Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems
JF  - Communications on Pure and Applied Analysis
N2  - In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered to reconstruct the estimator from the random noisy data. In this statistical learning setting, we derive the rates of convergence for the regularized solution under certain assumptions on the nonlinear forward operator and the prior assumptions. We discuss estimates of the reconstruction error using the approach of reproducing kernel Hilbert spaces.
KW  - Statistical inverse problem
KW  - Tikhonov regularization
KW  - Hilbert Scales
KW  - reproducing kernel Hilbert space
KW  - minimax convergence rates
Y1  - 2020
U6  - https://doi.org/10.3934/cpaa.2020183
SN  - 1534-0392
SN  - 1553-5258
VL  - 19
IS  - 8
SP  - 4111
EP  - 4126
PB  - American Institute of Mathematical Sciences
CY  - Springfield
ER  -