Distribution of Random Numbers
<p>I have two options of code:</p>

<p><strong>Option 1</strong></p>

<pre><code>int myFunc() {
  return new Random().nextInt();
}
</code></pre>

<p>Or:</p>

<p><strong>Option 2</strong></p>

<pre><code>private static final Random random = new Random();

int myFunc() {
  return random.nextInt();
}
</code></pre>

<p>I understand that <code>option 2</code> is more idiomatic. I am wondering about the validity of <code>option 1</code>.</p>

<p>In <code>option 1</code> I will only ever use the first number generated by a given seed. In <code>option 2</code> I choose a seed and generate <code>n</code> numbers using that seed. IIUC the guarantees on randomness are on this use case.</p>

<p>My question is, therefore, if I call <code>option 1</code> many times are there any guarantees on the uniformity of the distribution of the output?</p>