We study the dynamics of a tracer particle (TP) on a comb lattice populated by randomly moving hard-core particles in the dense limit. We first consider the case where the TP is constrained to move on the backbone of the comb only. In the limit of high density of the particles, we present exact analytical results for the cumulants of the TP position, showing a subdiffusive behavior ∼t^{3/4}. At longer times, a second regime is observed where standard diffusion is recovered, with a surprising nonanalytical dependence of the diffusion coefficient on the particle density. When the TP is allowed to visit the teeth of the comb, based on a mean-field-like continuous time random walk description, we unveil a rich and complex scenario with several successive subdiffusive regimes, resulting from the coupling between the geometrical constraints of the comb lattice and particle interactions. In this case, remarkably, the presence of hard-core interactions asymptotically speeds up the TP motion along the backbone of the structure.

Diffusion and Subdiffusion of Interacting Particles on Comblike Structures.

We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatiotemporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first-passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.

Heterogeneous continuous-time random walks.

Realized volatility forecasting: Robustness to measurement errors

A combined dynamics consisting of Brownian motion and Levy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and Levy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Levy flights with stable exponent $\alpha<1$, by itself implying zero probability of hitting a point on a line, lead to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent $\alpha$ of the Levy flight component.

Search reliability and search efficiency of combined L\'evy-Brownian motion: long relocations mingled with thorough local exploration

We study the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. We deduce analytical expressions for the stationary occupation probability and for the mean and global first passage times. This general approach allows us to characterize the effect of resetting on the capacity of random walk strategies to reach a particular target or to explore the network. Our formalism holds for ergodic random walks and can be implemented from the spectral properties of the random walk without resetting, providing a tool to analyze the efficiency of search strategies with resetting to multiple nodes. We apply the methods developed here to the dynamics with two reset nodes and derive analytical results for normal random walks and L\'evy flights on rings. We also explore the effect of resetting to multiple nodes on a comb graph, L\'evy flights that visit specific locations in a continuous space, and the Google random walk strategy on regular networks.

Diffusive transport on networks with stochastic resetting to multiple nodes.

Encounters between walkers performing a random motion on an appropriate structure can describe a wide variety of natural phenomena ranging from pharmacokinetics to foraging. On homogeneous structures the asymptotic encounter probability between two walkers is (qualitatively) independent of whether both walkers are moving or one is kept fixed. On infinite comblike structures this is no longer the case and here we deepen the mechanisms underlying the emergence of a finite probability that two random walkers will never meet, while one single random walker is certain to visit any site. In particular, we introduce an analytical approach to address this problem and even more general problems such as the case of two walkers with different diffusivity, particles walking on a finite comb and on arbitrary bundled structures, possibly in the presence of loops. Our investigations are both analytical and numerical and highlight that, in general, the outcome of a reaction involving two reactants on a comblike architecture can strongly differ according to whether both reactants are moving (no matter their relative diffusivities) or only one is moving and according to the density of shortcuts among the branches.

/pdf/two-particle-problem-in-comblike-structures-2snjy2mzzz.pdf

Two-particle problem in comblike structures.

In this paper we adopt Adaptive Lasso techniques in vector Multiplicative Error Models (vMEM), and we show that they provide asymptotic consistency in variable selection and the same efficiency as ...

Adaptive Lasso for vector Multiplicative Error Models

A SHARP model of bid–ask spread forecasts

We analyze price transmission dynamics in the under-investigated feed supply chain, applying a special case of the Threshold Vector Error Correction model where the cointegrating relationship is interrupted. Weekly Italian dairy feed and corn prices are used, finding evidence of asymmetric price transmission when the feed industry's margins are squeezed and highly volatile. The proposed Interrupted Threshold Cointegration model represents a valid complement to existing threshold and regime-switching techniques, allowing for the application of an agile nonstructural error correction model when standard cointegration tests fail to detect any long-run relationship between price series. [EconLit Citations: Q11, Q13, C24]. 

https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/agr.21797

When cointegration is interrupted: Price transmission analysis in the Italian dairy‐feed industry

We consider a particle performing a stochastic motion on a one-dimensional lattice with jump widths distributed according to a power-law with exponent $\mu + 1$. Assuming that the walker moves in the presence of a distribution $a(x)$ of targets (traps) depending on the spatial coordinate $x$, we study the probability that the walker will eventually find any target (will eventually be trapped). We focus on the case of power-law distributions $a(x) \sim x^{-\alpha}$ and we find that as long as $\mu < \alpha$ there is a finite probability that the walker will never be trapped, no matter how long the process is. This analytical result, valid on infinite chains, is corroborated by numerical simulations which also evidence the emergence of slow searching (trapping) times in finite-size system. The extension of this finding to higher-dimensional structures is also discussed.

L\'evy flights with power-law absorption

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