Lower bound on the size-Ramsey number of tight paths

The size-Ramsey number R⁽ᵏ⁾(H) of a k-uniform hypergraph H is the minimum number of edges in a k-uniform hypergraph G with the property that each $2$-edge coloring of G contains a monochromatic copy of H. For k≥2 and n, a k-uniform tight path on n vertices P⁽ᵏ⁾n,k-1 is defined as a k-uniform hypergraph on n vertices for which there is an ordering of its vertices such that the edge set consists of all k-element intervals of consecutive vertices in this ordering. We show a lower bound on the size-Ramsey number of k-uniform tight paths, which is, considered assymptotically in both the uniformity k and the number of vertices n, R⁽ᵏ⁾(P⁽ᵏ⁾n,k-1)= Ωn,k(log (k)n).