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Unit# Stochastic process chair

Chair

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Random walk

In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space.
An elementary example of a random walk is the rando

Random graph

In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which

Process

A process is a series or set of activities that interact to produce a result; it may occur once-only or be recurrent or periodic.
Things called a process include:
Business and management

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We photoexcite high-energy holon-doublon pairs as a way to alter the magnetic free energy landscape and resulting phase diagram of the frustrated honeycomb magnet ??-RuCl3. The pair recombination through multimagnon emission is tracked through the time evolution of the magnetooptical response originating from ??-RuCl3???s competing zigzag spin-ordered ground state. A small holon-doublon density suffices to reach a spin-disordered state. The phase transition is described within a dynamical Ginzburg-Landau framework, corroborating the quasistationary nature of the transient phase. Our work suggests a new route to reach a nontrivial spin-disordered state in Kitaev-like magnets.

We consider the asymmetric exclusion process with a driven tagged particle on Z which has different jump rates from other particles. When the non-tagged particles have non-nearest-neighbor jump rates , we show that the tagged particle can have a speed which has a different sign from the mean derived from its jump rates. We also show the existence of some non-trivial invariant measures for the environment process viewed from the tagged particle. Our arguments are based on coupling, martingale methods, and analyzing currents through fixed bonds.

alpha-RuCl3 is a promising candidate material to realize the so far elusive quantum spin liquid ground state. However, at low temperatures, the coexistence of different exchange interactions couple the effective pseudospins into an antiferromagnetically zigzag (ZZ) ordered state. The low-field evolution of spin structure is still a matter of debate and the magnetic anisotropy within the honeycomb planes is an open and challenging question. Here, we investigate the evolution of the ZZ order parameter by second-order magneto-optical effects, the magnetic linear dichroism and magnetic linear birefringence. Our results clarify the presence and nature of metamagnetic transitions in the ZZ phase of alpha-RuCl3. The experimental observations show the presence of initial magnetic domain repopulation followed by a spin-flop transition for small in-plane applied magnetic fields (approximate to 1.6 T) along specific crystallographic directions. In addition, using a magneto-optical approach, we detected the recently reported emergence of a field-induced intermediate phase before suppressing the ZZ order. The results disclose the details of various angle-dependent in-plane metamagnetic transitions quantifying the bond-anisotropic interactions present in alpha-RuCl3.