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We consider the model space of constant curvature in dimension n and characterize all co-adapted couplings of Brownian motions on this space for which the distance between the processes is deterministic. In addition, the construction of the…
The phenomenology of the modified Newtonian dynamics (MOND) can be recovered from a mechanism of "gravitational polarization" of some dipolar medium playing the role of dark matter. We review a relativistic model of dipolar dark matter…
Hyperuniform many-body systems in $d$-dimensional Euclidean space are characterized by completely suppressed (normalized) infinite-wavelength density fluctuations, and appear to be endowed with novel exotic physical properties. In this…
Nonmagnetic particles in a carrier ferrofluid acquire an effective dipolar moment when placed in an external magnetic field. This fact leads them to form chains that will roughen due to Brownian motion when the magnetic field is decreased.…
Consider a semimartingale reflecting Brownian motion (SRBM) $Z$ whose state space is the $d$-dimensional nonnegative orthant. The data for such a process are a drift vector $\theta$, a nonsingular $d\times d$ covariance matrix $\Sigma$, and…
In any dimension $D$, the Euclidean Einstein-Hilbert action, which describes gravity in the absence of matter, can be discretized over random discrete spaces obtained by gluing families of polytopes together in all possible ways. In the…
In this paper, we present a theory to efficiently deal with mechanical properties of heterogeneous polymer chain in free space and the central problem is to evaluate the diffusion equation and orientation-orientation correlation function,…
We argue that the natural framework for embedding the ideas of deformed, or doubly, special relativity (DSR) into a curved spacetime is a generalisation of Einstein-Cartan theory, considered by Stelle and West. Instead of interpreting the…
In computer vision and medical imaging, the problem of matching structures finds numerous applications from automatic annotation to data reconstruction. The data however, while corresponding to the same anatomy, are often very different in…
This work deals with the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. If the potential has no inversion symmetry and its fluctuations are asymmetric and correlated in time, a net flow can be generated…
This paper concerns the intermediate dimensions, a spectrum of dimensions that interpolate between the Hausdorff and box dimensions. Potential theoretic methods are used to produce dimension bounds for images of sets under H\"older maps and…
The classical Einstein-Langevin theory of Brownian motion assumes a memoryless thermal bath, establishing a universal fractal dimension of $d_v = 3/2$ for the velocity fluctuations of a particle. In this Letter, we demonstrate…
Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the…
We introduce and study a generalization of the classical weighted Bergman and Dirichlet spaces on the unit ball in high dimension, the Bergman-Dirichlet spaces. Their counterparts on the whole $n$-complex space, the Bargmann-Dirichlet…
We examine vacuum fluctuations in theories with modified dispersion relations which represent dimensional reduction at high energies. By changing units of energy and momentum we can obtain a description rendering the dispersion relations…
Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A…
Defects between gapped boundaries provide a possible physical realization of projective non-abelian braid statistics. A notable example is the projective Majorana/parafermion braid statistics of boundary defects in fractional quantum…
Brownian motion may be embedded in the Fock space of bosonic free field in one dimension.Extending this correspondence to a family of creation and annihilation operators satisfying a q-deformed algebra, the notion of q-deformation is…
We present a geometric interpretation of a product form stationary distribution for a $d$-dimensional semimartingale reflecting Brownian motion (SRBM) that lives in the nonnegative orthant. The $d$-dimensional SRBM data can be equivalently…
The scalar modes of the geometry induced by dimensional decoupling are investigated. In the context of the low energy string effective action, solutions can be found where the spatial part of the background geometry is the direct product of…