Related papers: Step Scaling with off-shell renormalisation
We present on shell-scheme for the 2PI formalism with a particular focus on the renormalized equations of motion. We first revisit the so-called Hartree approximation where we give the counterterms for both the broken and unbroken phase.…
The connection between anomalous scaling of structure functions (intermittency) and numerical methods for turbulence simulations is discussed. It is argued that the computational work for direct numerical simulations (DNS) of fully…
Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for…
We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…
Stochastic minimax optimization on Riemannian manifolds has recently attracted significant attention due to its broad range of applications, such as robust training of neural networks and robust maximum likelihood estimation. Existing…
We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide…
Recently several lattice collaborations have studied the scale dependence of the coupling in theories with different gauge groups and fermion representations using the Schr\"odinger functional method. This has motivated us to look at the…
Treating the fermionic ground state problem as a constrained stochastic optimization problem, a formalism for fermionic quantum Monte Carlo is developed that makes no reference to a trial wavefunction. Exchange symmetry is enforced by…
We propose a strategy for large volume non-perturbative renormalization which alleviates the window problem by reducing cut-off effects. We perform a proof-of-concept study using position space renormalization scheme and the CLS $N_f=2+1$…
For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach…
The main technical and conceptual features of the lattice $1/N$ expansion in the scaling region are discussed in the context of a two-parameter two-dimensional spin model interpolating between $CP^{N-1}$ and $O(2N)$ $\sigma$ models, with…
We develop an instantonic calculus to derive an analytical expression for the thermally-assisted tunneling decay rate of a metastable state in a fully connected quantum spin model. The tunneling decay problem can be mapped onto the Kramers…
The performance analysis of random vector channels, particularly multiple-input-multiple-output (MIMO) channels, has largely been established in the asymptotic regime of large channel dimensions, due to the analytical intractability of…
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…
Large-scale quantum devices provide insights beyond the reach of classical simulations. However, for a reliable and verifiable quantum simulation, the building blocks of the quantum device require exquisite benchmarking. This benchmarking…
We present classical and quantum mechanical descriptions of lattice dynamics, from the atomic to the continuum scale, using atomic scale symmetry modes and their constraint equations. This approach is demonstrated for a one-dimensional…
A scheme for stabilizing stochastic approximation iterates by adaptively scaling the step sizes is proposed and analyzed. This scheme leads to the same limiting differential equation as the original scheme and therefore has the same…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
Cooling methods and particle slowers as well as accelerators are basic tools for fundamental research and applications in different fields and systems. We put forward a generic mechanism to scale the momentum of a particle, regardless of…
In the context of relativistic heavy-ion collisions, we explore the stochastic and dissipative relaxational dynamics of a non-conserved order parameter in a $\lambda\varphi^4$ interaction. The cutoff of the theory is provided by the lattice…