Related papers: Small Noise Perturbations in Multidimensional Case
We present a perturbation method for determining the moment stability of linear ordinary differential equations with parametric forcing by colored noise. In particular, the forcing arises from passing white noise through an $n$th order…
We consider a dissipative vector field which is represented by a nearly-integrable Hamiltonian flow to which a non symplectic force is added, so that the phase space volume is not preserved. The vector field depends upon two parameters,…
The phase space for a periodically driven nonlinear oscillator consists of many resonance zones. Let the strength of periodic excitation and the strength of the damping be indexed by a small parameter $\varepsilon$. It is well known that,…
This paper proves an analogue of a result of Banuelos and Sa Barreto on the asymptotic expansion for the trace of Schrodinger operators on $\R^d$ when the Laplacian $\Delta$, which is the generator of the Brownian motion, is replaced by the…
Given a linear semi-bounded symmetric operator $S\ge -\omega$, we explicitly define, and provide their nonlinear resolvents, nonlinear maximal monotone operators $A_\Theta$ of type $\lambda>\omega$ (i.e. generators of one-parameter…
We investigate quasinormal mode frequencies $\omega_n$ of gravitinos and generic massive spin-3/2 fields in a Schwarzschild-AdS$_D$ background in spacetime dimension $D>3$, in the black brane (large black hole) limit appropriate to many…
We study noise induced switching in systems far from equilibrium by using an underdamped micromechanical torsional oscillator driven into the nonlinear regime. Within a certain range of driving frequencies, the oscillator possesses two…
A low noise constant current source used for measuring the $1/f$ noise in disordered systems in ohmic as well as non-ohmic regime is described. The source can supply low noise constant current starting from as low as 1 $\mu$A to a few tens…
We consider asymptotic stability of a small solitary wave to supercritical 2-dimensional nonlinear Schr\"{o}dinger equations $$ iu_t+\Delta u=Vu\pm |u|^{p-1}u \quad\text{for $(x,t)\in\mathbb{R}^2\times\mathbb{R}$,}$$ in the energy class.
This letter presents a high-dimensional analysis of the training dynamics for a single-layer nonlinear contrastive learning model. The empirical distribution of the model weights converges to a deterministic measure governed by a…
We consider a well-known family of SDEs with irregular drifts and the correspondent zero noise limits. Using (mollified) local times, we show which trajectories are selected. The approach is completely probabilistic and relies on elementary…
Studies on the finite amplitude stability of pipe flows identified a range of different scaling exponents between $\beta\approx -1 $ and $\beta\approx-1.5$, relating $A\sim Re^{\beta}$, where $A$ is the minimum amplitude of disturbance to…
The well-posedness is established for McKean-Vlasov SDEs driven by $\alpha$-stable noises ($1<\alpha<2$). In this model, the drift is H\"{o}lder continuous in space variable and Lipschitz continuous in distribution variable with respect to…
We consider the ordinary differential equation (ODE) $dx_{t} =b(t,x_{t} ) dt+ dw_{t}$ where $w$ is a continuous driving function and $b$ is a time-dependent vector field which possibly is only a distribution in the space variable. We…
Nonclassical noises over the plane (such as the black noise of percolation) consist of sigma-fields corresponding to some planar domains. One can treat less regular domains as limits of more regular domains, thus extending the noise and its…
Off-lattice DLA clusters grown with different levels of noise reduction are found to be consistent with a simple fractal fixed point. Cluster shapes and their ensemble variation exhibit a dominant slowest correction to scaling, and this…
Sustained oscillations (SOs) are commonly observed in systems dominated by converters. Under specific conditions, even though the origin of SOs can be identified through negative damping modes using conventional linear analysis, utilizing…
We study the convergence properties of the conditional (Kullback-Leibler) entropy in stochastic systems. We have proved very general results showing that asymptotic stability is a necessary and sufficient condition for the monotone…
The absolutely continuous spectrum of one-dimensional Schr\"odinger operators is proved to be stable under perturbation by potentials satisfying mild decay conditions. In particular, the absolutely continuous spectrum of free and periodic…
A perturbation theory for the Nonlinear Schroedinger Equation (NLSE) in 1D on a lattice was developed. The small parameter is the strength of the nonlinearity. For this purpose secular terms were removed and a probabilistic bound on small…