相关论文: Quadratic and rate-independent limits for a large-…

We study gradient flows of general functionals with linear growth with very weak assumptions. Classical results concerning characterisation of solutions require differentiability of the Lagrangian, as for the time-dependent minimal surface…

We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…

We study the motion of a particle in a random time-dependent vector field defined by the 2D Navier-Stokes system with a noise. Under suitable non-degeneracy hypotheses we prove that the empirical measures of the trajectories of the pair…

The large deviation principle on phase space is proved for a class of Markov processes known as random population dynamics with catastrophes. In the paper we study the process which corresponds to the random population dynamics with linear…

This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…

The configuration model is a sequence of random graphs constructed such that in the large network limit the degree distribution converges to a pre-specified probability distribution. The component structure of such random graphs can be…

We study a single server FIFO queue that offers general service. Each of n customers enter the queue at random time epochs that are inde- pendent and identically distributed. We call this the random scattering traffic model, and the…

We study the statistics of the relative separation between two fluid particles in a spatially smooth and temporally random flow. The Lagrangian strain is modelled by a telegraph noise, which is a stationary random Markov process that can…

In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external…

Particle segregation is common in natural and industrial processes involving flowing granular materials. Complex, and seemingly contradictory, segregation phenomena have been observed for different boundary conditions and forcing. Using…

We consider in this work small random perturbations (of multiplicative noise type) of the gradient flow. We prove that under mild conditions, when the potential function is a Morse function with additional strong saddle condition, the…

The Whittaker 2d growth model is a triangular continuous Markov diffusion process that appears in many scientific contexts. It has been theoretically intriguing to establish a large deviation principle for this 2d process with a scaling…

We present a systematic derivation of the gradient flows associated to a broad class of interfacial energies, emphasizing the relation between intrinsic and extrinsic variations of the interface. We show that the intrinsic variables…

We examine the stationary--state equations for lattices with generalized Markovian dephasing and relaxation. When the Hamiltonian is quadratic, the single--particle correlation matrix has a closed system of equations even in the presence of…

The so-called 'Level 2.5' general result for the large deviations of the joint probability of the density and of the currents for Markov Jump processes is applied to the case of $N$ independent particles on a ring with random transition…

This is an overview about natural sample spaces for differential equations driven by various noises. Appropriate sample spaces are needed in order to facilitate a random dynamical systems approach for stochastic differential equations. The…

We formulate and study a stochastic model for the thermally-driven motion of interacting straight screw dislocations in a cylindrical domain with a convex polygonal cross-section. Motion is modelled as a Markov jump process, where waiting…

We consider a system-reservoir model where the reservoir is modulated by an external noise. Both the internal noise of the reservoir and the external noise are stationary, Gaussian and are characterized by arbitrary decaying correlation…

The stochastic scenario of relaxation in the complex systems is presented. It is based on a general probabilistic formalism of limit theorems. The nonexponential relaxation is shown to result from the asymptotic self-similar properties in…

Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time…