activity
20152026
most citedThe random walk on the random connection model

4 citations · 15 across the 14 of their papers we have counts for

collaborators

14 papers

math.PR2026

Regularization of Hyperbolic Stochastic Partial Differential Equations By Two Fractional Brownian Sheets

Rachid Belfadli, Youssef Ouknine, Ercan Sönmez

In this paper, we establish existence and uniqueness of strong solutions for a stochastic differential equation driven by an additive noise given by the sum of two correlated fract…

math.PR2024★ 1 cited

Intersection probabilities for flats in hyperbolic space

Ercan Sönmez, Panagiotis Spanos, Christoph Thäle

Consider the -dimensional hyperbolic space of constant curvature and fix a point playing the role of an origin. Let be a uniform random $…

math.PR2023★ 1 cited

On the distances within cliques in a soft random geometric graph

Ercan Sönmez, Clara Stegehuis

We study the distances of edges within cliques in a soft random geometric graph on a torus, where the vertices are points of a homogeneous Poisson point process, and far-away point…

math.PR2022★ 2 cited

On the existence and regularity of local times

Tommi Sottinen, Ercan Sönmez, Lauri Viitasaari

We study the existence and regularity of local times for general -dimensional stochastic processes. We give a general condition for their existence and regularity properties. To…

math.PR2022★ 2 cited

The longest edge of the one-dimensional soft random geometric graph with boundaries

Arnaud Rousselle, Ercan Sönmez

The object of study is a soft random geometric graph with vertices given by a Poisson point process on a line and edges between vertices present with probability that has a polynom…

math.PR2022

Persistence probabilities of mixed FBM and other mixed processes

Frank Aurzada, Martin Kilian, Ercan Sönmez

We consider the sum of two self-similar centred Gaussian processes with different self-similarity indices. Under non-negativity assumptions of covariance functions and some further…

math.PR2021

The longest edge in discrete and continuous long-range percolation

Arnaud Rousselle, Ercan Sönmez

We consider the random connection model in which an edge between two Poisson points at distance is present with probability . We conduct an extreme value analysis on this…

math.PR2020★ 1 cited

On mixed fractional SDEs with discontinuous drift coefficient

Ercan Sönmez

We prove existence and uniqueness of the solution for a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional…

math.PR2019★ 1 cited

Graph distances of continuum long-range percolation

Ercan Sönmez

We consider a version of continuum long-range percolation on finite boxes of in which the vertex set is given by the points of a Poisson point process and each pair…

math.PR2019★ 4 cited

The random walk on the random connection model

Ercan Sönmez, Arnaud Rousselle

We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices and are connected with probability that asympt…

math.PR2018★ 1 cited

Max-linear models in random environment

Claudia Klüppelberg, Ercan Sönmez

We extend previous work of max-linear models on finite directed acyclic graphs to infinite graphs as well as random graphs, and investigate their relations to classical percolation…

math.PR2017

On the carrying dimension of occupation measures for self-affine random fields

Peter Kern, Ercan Sönmez

Hausdorff dimension results are a classical topic in the study of path properties of random fields. This article presents an alternative approach to Hausdorff dimension results for…

math.PR2016★ 2 cited

Fractal behavior of multivariate operator-self-similar stable random fields

Ercan Sönmez

We investigate the sample path regularity of multivariate operator-self-similar stable random fields with values in given by a harmonizable representation. Such fiel…

math.PR2015

Sample path properties of generalized random sheets with operator scaling

Ercan Sönmez

We consider operator scaling -stable random sheets, which were introduced in [12]. The idea behind such fields is to combine the properties of operator scaling -stable random…