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We define and prove the existence of a fractional Brownian motion indexed by a collection of closed subsets of a measure space. This process is a generalization of the set-indexed Brownian motion, when the condition of independance is…
The conformational properties of flexible and semiflexible polymers exposed to active noise are studied theoretically. The noise may originate from the interaction of the polymer with surround- ing active (Brownian) particles or from the…
We study semi-martingale obliquely reflected Brownian motion with drift in the first quadrant of the plane in the transient case. Our main result determines a general explicit integral expression for the moment generating function of…
We introduce methods for large scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method at a cost comparable to the…
We study a directed polymer model in a random environment on infinite binary trees. The model is characterized by a phase transition depending on the inverse temperature. We concentrate on the asymptotics of the partition function in the…
A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work we study a 2D version of this model, where the molecule is a heavy disk of mass M and the gas is…
Solving the stationary nonlinear Fokker-Planck equations is important in applications and examples include the Poisson-Boltzmann equation and the two layer neural networks. Making use of the connection between the interacting particle…
Nonlinear convection structures are investigated in quantitative detail as a function of Rayleigh number for several negative and positive Soret coupling strengths (separation ratios) and different Lewis and Prandtl numbers characterizing…
We present three sets of results for the stationary distribution of a two-dimensional semimartingale reflecting Brownian motion (SRBM) that lives in the nonnegative quadrant. The SRBM data can equivalently be specified by three geometric…
Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of…
This paper provides information about the asymptotic behavior of a one-dimensional Brownian polymer in random medium represented by a Gaussian field $W$ on ${\mathbb{R}}_+\times{\mathbb{R}}$ which is white noise in time and function-valued…
We discuss the two-dimensional motion of a Brownian particle that is confined to a harmonic trap and driven by a shear flow. The surrounding medium induces memory effects modelled by a linear, typically nonreciprocal coupling of the…
We show that the partition function of the multi-layer semi-discrete directed polymer converges in the intermediate disorder regime to the partition function for the multi-layer continuum polymer introduced by O'Connell and Warren. This…
We study the stationary reflected Brownian motion in a non-convex wedge, which, compared to its convex analogue model, has been much rarely analyzed in the probabilistic literature. We prove that its stationary distribution can be found by…
Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or regularity) and expanding the breadth of its…
We study the directed polymer model in a bounded environment with bond disorder and show that, in the interior of the weak disorder phase, weak disorder continues to hold upon perturbation by a small bias. Using this stability result, we…
Starting from the microscopic Smoluchowski equation for interacting Brownian particles under stationary shearing, exact expressions for shear-dependent steady-state averages, correlation and structure functions, and susceptibilities are…
Consider non-intersecting Brownian motions on the real line, starting from the origin at t=0, with a number of particles forced to reach p distinct target points at time t=1. This work shows that the transition probability, that is the…
We present in this paper the construction of a continuum directed polymer model in an environment given by space-time L\'evy noise. One of the main objectives of this construction is to describe the scaling limit of discrete directed…
This paper provides information about the asymptotic behavior of a one-dimensional Brownian polymer in random medium represented by a space-time Gaussian field W assumed to be white noise in time and function-valued in space. According to…